Absurdly Youthful Father: What most human characters think Oga is. However, none of the demons ever point out that it's weird a teenager got chosen to foster Beel.
Accidental Kiss: One happens between Hilda and Baby Beel in Chapter 176, which makes Hilda revert back to her post-memory loss personality.
Accidental Misnaming: Izo calling Oga 'Madason'. In his defence, Oga did originally introduce himself like this.
Accidental Truth: The Akuma Academy story that Furuichi told the rest of the delinquents, when an actual Akuma Academy was introduced.
Action Girl: Hilda, Kunieda and the entire Red Tails gang.
Actually That's My Assistant: Oga thinks Lamia is the imperial doctor, and she plays along with it, until the real doctor comes and smacks her for trying to hog the spotlight.
A more minor variant is when Izo mistakes Tojo for the leader of the delinquents due to the fact that he's the strongest of the Tōhōshinki.
A-Cup Angst: Aoi; her chest bothers her slightly, particularly when she's compared to Hilda. The other Red Tail girls seem to feel the same way during their communal bath.
Koma: Calm down. Whether they're massive or itty bitty, I love all tits. Aoi:ITTYBITTY!?
Adult Fear: The link between Oga and Beel gets cut, and Beel seemingly vanishes. Oga's panicked expression says it all.
Adults Are Useless: When hearing about Oga's involvement in a gang war, his mother says "You got in another fight? Seriously? Well, I guess you'll take care of it".
There's also the fact that everyone just assumes Oga and Kunieda are teen parents, without actually trying to get the details straight.
Saotome starts getting hit with this, since while he'll teach the kids, you have to wonder why he, the man Behemoth described as a One-Man Army, doesn't ever even try to help them out when say, Lucifer shows up.
Affectionate Parody: Of tournament arcs (especially at the end of the En arc), standard shonen, and delinquent-based stories.
The volleyball match is one big homage to sports manga. This is especially obvious in the anime, with the liberal use of anime effects and dramatic, rousing music.
Aliens Speaking English: This is lampshaded by Furuichi, who believes that Japanese is the native language of the Demon World simply because all the demons he's encountered can speak it fluently. Chapter 226 tells us that this is not the case, and reveals that the majority of demons use Translator Microbes to communicate. Hilda is actually the only person to play this trope straight, since she took the time to physically learn various Earth languages.
Hilda: Isn't it weird that they're in the same class as Oga? Kanzaki: What I want to know is... why the hell are you guys in that same class as me?
Always Second Best: The Upstart arc shows that Kanzaki has major issues with being seen as a lesser delinquent to Oga. His attempts to prove himself as Oga's equal lead him and Furuichi right into Nasubi'strap.
Amazon Brigade: The Red Tails. Their pledge is that if you get a boyfriend, you have to leave the group.
And then came the Red Tails' demon world counterpart made up of Pillars Agiel, Tiriel, Paimel, Fabas, and Elim.
From a filler episode with a rare form of said milk: "Not only does it change all the Demon Milk Proteins into safe to ingest Demon Peptides, it's gone through Demon Enzyme Digestion and Demon Membrane Filtering Treatment, and with its Demon Lipid Components, chiefly Demon Middle Chain Triglycerides, its Demon Essential Fatty Acids have been Demon Strengthened, Demon Combining the Demon Fructooligosaccarides and Demon Nucleosides, and more and more and more... into Demon Golden Yellow Broth!"
The Demon Lord's tissues, which allow the user to summon a demon from Behemoth's 34 Pillar Squad. They strengthen Furuichi so much that he can even take on Oga, Miki and Tojo.
Amusing Injuries: Any time Oga beats up some random mooks, or gets beaten up by Hilda. Or he gets electrocuted.
And the Adventure Continues: The epilogue starts with Oga's class' graduation, with most of his friends having previously graduated coming back for it. Then we find out Oga's been romping around the demon world fighting whoever he darn well pleases and has been given custody of Beel's new little sister, Nico, and Beel knows one new word after all this time.
Anti-Hero: Oga, when he can be considered a hero at all.
Arranged Marriage: Attributing to his immense wealth, Himekawa had been betrothed to marry Kugayama since birth. They were childhood friends and were close, at least until Kugayama outwitted Himekawa and took the Demon's Portrait, and was further strained when Himekawa ditched his old fancy academy to go to Ishiyama. Despite all this, she was apparently still in love with him all along.
It gets even more complicated. Kugayama fell in love with him during childhood, and in response her grandfather arranged the marriage. However she didn't want to reveal the fact that they were engaged to him, fearing that it would ruin the relationship they already had. Himekawa, who didn't know the identity of his fiancee (and possibly didn't know about her being a Bifauxnen), grew to value her as his Only Friend and thus felt betrayed when the truth came out. This is probably the reason he left the academy in the first place.
Being his first manga, you can really see the artist developing and becoming more comfortable with his style over time. Though it hasn't changed much, it's improved greatly, becoming smoother and cleaner with a great deal more detail (particularly in backgrounds) and effects.
Artifact of Death: The Demon's Portrait, the objective of the San Marx Fetch Quest, has a 50:50 chance of bringing either death or wealth to its owner.
It turns out to literally be a demon's portrait, that of Beel's mother painted by his father, it's pretty impressive considering his father's Cloud Cuckoo Lander personality.
Artificial Riverbank: A popular hang-out spot for Oga and Beel, and often where confrontations take place.
Authority Equals Asskicking: The Tohoshinki are the de facto leaders of Ishiyama High by virtue of being the strongest delinquents out there. Later on, they recognize Oga as their new "Chief" after the latter united Ishiyama by kicking all of their asses (except Kunieda, who fell in love with him).
The same applies for Behemoth's 34 Pillar Division. The Generals are all strong demons while their lackeys are pushover mooks.
Ass Shove: A warning for all Pillar Squadmooks: Don't try to mess with a pissed off Oga on a mission unless you want a spear up your ass.
Furuichi tries to be one in front of girls but he usually fails miserably and has to be bailed out by Oga. Post Demon Tissues and becoming the Delinquents' de facto tactician, he's well one his way to becoming one.
Balance of Power: Tōhōshinki, who are the four upperclassmen gang leaders that control Ishiyama High.
At least until Oga started unintentionally throwing everything out of whack by hospitalizing 2 of the 4 and unintentionally getting the 3rd to give up her title of leader, which creates an Evil Power Vacuum that the 4th unknowningly fills until he is defeated (again by Oga).
The very first teacher the kids get when they transfer to St. Ishiyama tries to use this to keep the kids in line by beating the strongest in the class in an arm wrestling match. Toobadthe in guy in question isTojo.
Since the Ishiyama students were spread around while the school was being rebuilt, neither Oga nor the Tōhōshinki were unable to keep them all the smaller groups of Ishiyama delinquents in line. Now over thirty different groups are vying for the top spot in the rebuilt Ishiyama, the six most notable and dangerous being led by freshmen, and they all plan on taking out those who went to Saint Ishiyama first. Not only that, but since Aoi quit her leadership spot and Nene was unable to keep an eye on all of the Red Tails, some have branched out and created an entirely new group, lead by someone who Aoi knew was going to do something like this eventually.
Bald of Evil: The students from Teimo, most of whom apparently are bald, rather than skinheads.
Bandage Babe: Aoi has these covering much of her arms and chest in Chapter 192, which shows us just how much of a Curb-Stomp Battle her fight with the splinter group of Red Tails was. In her defense, she refused to fight against them. They didn't care and she got hammered anyway.
Bandaged Face: Pillar Odonel, made even more poignant by the fact that the bandages are tattooed, cover his entire head and his arms are chained to his sides.
Bare Your Midriff: Aoi at first, more than a few of the Red Tails women, and demons Satura, Agiel, Pamiel, Ananta and Lunana.
Betty and Veronica: Although Oga doesn't really care that much about either of them, romance-wise, Aoi (who is dark-haired) would fit as Betty while the blonde Hilda would be the Veronica. Likewise, the Betty for Beel would be Chiyo, with Futaba as the Veronica.
Kugayama is revealed to be one, even wearing a male uniform.
Big Bad: The Tohoshinki for the first few arcs, then Izuma for the St. Ishiyama arc, then Behemoth for the Akuma Academy arc, then Kugayama for the San Marx arc, then the Upstarts for the Return to Ishiyama arc.
Bigger Bad: The Solomon Company, which has ties to the last two on the list.
Big Damn Heroes: Natsume seems to have turned this into a habit, though his intentions still aren't entirely clear.
In Chapter 135, practically THE ENTIRE DAMN SCHOOL. Might be a subversion. Sure they certainly have a big damn entrance, but the games they were supposed to complete get overridden by Jabberwock and his personal Pillars hold them up so they don't manage to interfere with his and Oga's showdown. Overall, they do zilch. Lampshaded repeatedly afterwards.
Kaoru: We didn't get to do much in the last fight. Izuma: You burnt down the school pretty quickly after we arrived. Shizuka: Us arriving was supposed to be the big climax!
Kanzaki gets another one in Chapter 216, after he gets powered up by Beel. Though it's subverted, as the main reason he joins the fight is to get information on where the power sealing device is, rather than to bail out the other delinquents.
HIMEKAWA. Taken up to eleven in the anime, where the sparkles seem to be automatic and multiply the moment he does... well, anything.
Furuichi, after discovering the power of the Demon Lord's tissues. Like in all other appearances of the trope, it's lampshaded.
Nene: ...Your complexion doesn't look too good.
Bishōnen: Athrun, Alex, and Natsume to some extent.
Plenty of demons. Pillar Heads Naga, Salamander, and maybeVritra, Pillar Hecadoth on a good day, and now Pillar Schethalim has joined them as well. He even gets a nude scene that turns into Fan Disservice after losing to Oga at sudoku!
Baby Beel seems to think Oga looks and acts like this. So does Oga himself.
The mastermind who looks to be working for the Solomon Company. Just look.
Furuichi, depending on whether or not he's being a butt monkey at the time.
While on the plane to Okinawa, Shinjo asks why the Ishiyama group look so serious and angry, to which Oga replies that they're excited. Tojo tells him to shut up in case they're looked down upon. He seems raring to go.
Oga introducing himself and Beel to Izo as Madason and Nimzo. It takes Izo a while to realize he's been duped.
Blind Without 'Em: The MK5 become the MK4 when one of their members steps on his glasses and therefore cannot see a thing. The ridiculousness of this is pointed out by the other characters.
Bloodbath Villain Origin: Takamiya's origin is a slightly downplayed version of this; he became the angsty, screwed up person he is today after Lucifer left his father and his coworkers comatose shortly after he formed a contract with her. The visuals aren't downplayed, however, so it comes off as this played absolutely straight.
Happens to Furuichi, Hilda, and Oga in Beel's body when Baby Beel in Oga's body chooses Aoi over Hilda.
Happens again in Chapter 168 when Oga tries to do a comedic bit mimicking Kugayama as she revealed her true gender and love for Himekawa and Himekawa when he learns of Kugayama's true feelings for him.
Happens far more seriously to Furuichi in Chapter 207 when he is stabbed and has his heart ripped out by Lucifer. And then again to Oga, after being sealed from Beel's power, who outright vomits the stuff out. Aoi also gets in on the action, after combining the powers of the King's Crest and her Black Tech to launch a last ditch attack after Oga's powers fail.
Blood Knight: Oga, Tojo, Agiel, and possibly Baby Beel himself.
Izo seems to avert this, as he tends to beat up his own gang members for starting fights rather than retaliating against the opposing side and is the only character in the series so far to turn down a fight against Tojo. The only reason he's even at Oga's throat is because he sees him as a rival for Aoi's affections.
Blood Oath: It is revealed that to make a full contract with a demon, the demon must consume some of the potential contractor's blood.
Blood Upgrade: Baby Beel, who will electrocute everyone in the vicinity at the mere sight of blood, whether it's his or not.
Bodyguard Crush: From the way she blushes around him, it can be assumed Pillar Lunana feels this way about Jabberwock.
Body Horror: Don't let Baby Beel get too excited... your arm might explode.
Boke and Tsukkomi Routine: Oga's boke to Furuichi's tsukkomi. The series even plays on this from the very start of the first chapter/first episode.
This is switched around in Oga's dream sequence, where Oga plays the role of the straight man to everybody else's absurdity.
Boobs of Steel: Hilda is the currently strongest woman introduced, and by far the bustiest. Isabella and Yolda may rival her though (in bustiness, not strength). The one Hilda sees as her current 'rival', however, is Kunieda.
Book Dumb: Apparently all of Ishiyama High. They "hate studying 180 percent!" and Furuichi got the highest on the standardized test (a 59). And as Furuichi mentioned earlier, the test was on elementary school subjects.
Moves into Informed Flaw territory for some of the delinquents. In particular Natsume and Himekawa are shown to be very intelligent in other episodes (though Natsume didn't seem to study and Himekawa still cheated on the test like everyone else). It was probably just Rule of Funny at work, though.
Book Ends: The Okinawa trip both starts and ends with Alex being roped in to deal with the delinquents' holiday shenanigans.
Bowdlerise: In the original manga, one of MK5 pulled a gun on Nene and seemed about to shoot her. The anime changes it to having him prepare to punch her, which made her reaction of despair pretty uncalled for. Also, the way Natsume takes out the whole gang in the manga is far more violent and involves a lot of blood, whereas the anime version just cuts to them lying unconscious at his feet.
Basically all of the blood was removed, even though the manga isn't that gory and blood is only shed when things become really dangerous. It looks plain ridiculous when Oga can get stabbed in the side with a spear and come away with nothing but a ripped shirt.
Animax-South East Asia actually had ALL anime episodes edited for re-broadcast in the region with Baby Beel wearing a diaper.
Brainwashed: Pillar Head Salamander tries to do this to Oga and Tojo. It fails.
En and Futaba too, as the former is a prince who's used to being spoiled while the latter is simply a Spoiled Brat.
Breaking the Fellowship: Occurs in Chapter 231, after Oga chooses to let Beel go back to the Demon World with his mother.
Breaking the Fourth Wall: Though several characters endanger it, Kanzaki outright smashes the fourth wall when he complains about being given a tiny panel while trying to make a dramatic speech.
Tojo turns up during a dream sequence in Chapter 124 and mentions that he's been Out of Focus lately. The others reply that he's out-of-character and it's been so long no one even remembers him any more.
Furuichi does this after the ending animation in Episode 33.
Happens quite a bit in the End of War 4 episodes, particularly Nene who wonders why her avatar is still alive when she died oh-so dramatically in the previous episode. Also, Natsume takes a peek at the chainsaw carnage done on Shiroyama and cheerfully announces that they can't show it to viewers.
In Episode 54, Giant Baby Beel starts to tear off Giant Black Baby Beel's wings and Furuichi declares that they can't show that on TV, with the animation replaced by a scene with Alaindelon.
Tamapochi in Chapter 164, after Oga avoids her attack.
Tamapochi: Please read the mood! That was the scene where you get hit and start spurting blood!
Oga in Chapter 173 when he and Furuichi finally start their fight after several pages of small talk.
Oga: Stop wasting panels, goddammit!
When Tojo and Shizuka get introduced for their Best Couple Grand Prix challenge in Chapter 182, they have a massive panel dedicated to them. Cut to their opponents, a minor background couple, who are complaining about their (much smaller) panel.
Himekawa accidentally dropping Kamiya off a hotel roof.
Lackey: Thank God, it looks gag-like.
When Takamiya fights Furuichi, he talks about the tendency for manga characters to get a convenient power-up when pushed into a corner. Then, after he's beaten Furuichi half to death, he says it would make for a good manga-like scenario wherein Oga gets revenge.
The way Yuka introduces Natsume and Jinno when they arrive to help Kanzaki fight Himekawa.
Yuka: Natsume and Jinno are here! Nobody knows if these two are weak or strong; they're totally mysterious!
General Furuichi. During the Volleyball incident, Furuichi was included because he is obviously the mastermind and leader of these punks. Later on he has to recruit them all to help him, and succeeds. He really does become their leader, if only for a time.
He seems to be fully stepping into this role by the Upstart arc, to the point where's he's the one planning the delinquents' counterattack against the upstarts. Hecadoth even addresses him as 'Tactician' when he's summoned.
Bullying a Dragon: The punks that try and mess with Aoi's grandpa. Works about as well as one would expect.
Bunny-Ears Lawyer: Quite a few characters are shown to have their various quirks yet are all very competent: Oga himself is one of the strongest characters, yet carries a baby around with him. Dr. Furcas Rachmaninoff is one of the greatest demon doctors and chooses to take on the appearance of a blob wearing a fedora (his true form is vaguely shown to be rather badass). The Demon King himself is shown to be quite random and whimsical in his behaviour, yet is still, as his title implies, The Demon King.
Later arcs have the bus coming back for Behemoth's 34 Pillar Squad, thanks to Furuichi summoning them with the Demon Lord's tissues.
Suiten reappears in Chapter 181, as she's competing in the Best Couple Grand Prix with Mr. Saotome.
In Chapter 184, Izo Aiba turns up just in time to become Aoi's replacement partner in the Best Couple Grand Prix.
But Thou Must: When Oga's about to fight Tojo, Kanzaki and Himekawa offer to help gang up on Tojo. When he refuses, they respond by making the exact same offer, causing Oga to make the comparison to Dragon Quest.
Butt Monkey: Furuichi, oh so much. He's always either getting beaten up by Oga, beaten up by someone else, electrocuted by Baby Beel, roped into Oga's crazy schemes against his will and paying far more for them than anyone else, caught in compromising situations, or rejected by the ladies, and he generally seems to have the worst luck in the world.
In Chapter 143, Oga reveals that part of the reason he drags Furuichi everywhere because he thought it would be funny. Poor guy.
Chapter 173 thoroughly deconstructs this when the resulting psychological problems from his poor treatment cause him to snap, to the point where he doesn't even care if he dies anymore, so long as he gets to beat Oga. It counts as a brutal case of Reality Ensues, as the shit Furuichi gets put through would be an extremely severe case of bullying in Real Life.
This is hammered home in Chapter 212, when the six parts of his soul are identified as creepichi, mobichi, loli-ichi, bitchichi, furuchin and garbage respectively.
MK5 is definitely one. Despite the group's status as a gang of dangerous delinquents, the only purpose they serve is to be pounded down by both protagonists and antagonists. After their first appearance, it's their talent to "be beaten in the space of one page".
The poor guy who got hired to teach at Demon Academy. He has no idea why all his students are blatantly not high-school age, or why they have gills, or why they're organized like an army, or why they take orders from a little kid. He was unemployed, so he didn't really have any choice. Luckily, he's Genre Savvy enough to not rock the boat, so he probably survived until the school's destruction. Which means he needs a new job again.
Father Switch W! WOULD YOU FUCKING DIE ALREADY KICK!! Father Switch P! THE GREAT PUNCH OF OGA!!
Devil Shock, POMPADOUR SPECIAL!
The Cavalry: The 34 Pillar Division attempt to be this during Furuichi's fight against Takamiya, but fail miserably. It's later played straight a few chapters later when the rest of the Ishiyama gang storm the school to provide backup for Oga.
Cannot Spit It Out: Aoi and her feelings for Oga. Kumagawa couldn't tell Himekawa she loved him for years, but recently confessed.
Casanova Wannabe: Nobody can deny Furuichi has lots of enthusiasm. His success rate, on the other hand...
He finally gets some in Episode 53 of the anime. Too bad she's a ghost who only has eyes for the ghost that's possessing him...
Later, we're introduced to Mikagami of Teimo's Shadow Force.
Cast of Snowflakes: The massive cast of Mooks are all drawn uniquely, even those who are simply characters in the background waiting to get trounced by Oga. Quite a pleasant surprise granted they are all supposed to look like generic thugs, but each one manages to have several distinctive features in the drawing of their facial structures, scars, tattoos and piercings, hairstyles, musculature, clothing, and accessories. Of course, the wide variety of delinquenty scars, tattoos, etc. the author can pick and choose from helps.
Cerebus Retcon: Originally, it was said that the Demon King decided to destroy the human world because he was bored. Eventually it was revealed that he decided to do it because his wife had just left him. Or, rather, he still wanted to do it because he was bored, it's just that normally she would have been around to stop him.
Tojo and Kunieda are just as bad, being able to easily destroy concrete, throw people across rooms, break steel with their fists and run at supersonic speeds.
Chekhov's Gun: Tojo was briefly shown doing part-time work at a construction site. Turns out they were building Akuma Academy, and Tojo was sleeping there when Oga turned up.
The flimsy pack of tissues that Furuichi was initially furious at receiving from the Demon King as a reward turn out to have incredible summoning powers.
The Red Tails' restriction on not allowing its members to have boyfriends gets rescinded, setting the stage for Aoi's return as leader.
The third crest was an obvious one, but it still manged to be surprising. Himekawa reveals he had Oga's all along, but made it look like Takamiya's instead via a fake tattoo.
That build up of power right after the Tojo fight that destroyed the school the first time? Achieving that same buildup was Himekawa's plan all along as a Fake Defector.
Remember the Father Switch moves that Oga used against Jabberwock? They were his first attacks which fused the energies provided by the King's Crest and his Black Techs together. He later uses a more perfected fusion against Takamiya.
Chekhov's Gunman: Most of the apparently minor antagonists that Oga defeats early on later return to take active roles. Examples include Shimokawa, Kanzaki's Gang, Himekawa, the Red Tails, and Teimo. The anime also brings back several other denizens of Ishikawa.
Iris, Baby's Beel's mother, is a HUGE one. While she's first introduced in a throwaway appearance during the Demon Portrait arc, the Return to Ishiyama arc reveals that she's one of the key players in the Solomon Company, meaning that she's a potential traitor to the royal court, and possibly has enough power to force six of the Seven Deadly Sins into serving said company.
The Chessmaster: Himekawa. He realized that separating Oga from Beel causes a massive power buildup, as seen in the aftermath of the Tojo fight. So he faked a Face-Heel Turn, hid his King's Crest, and got a machine that seals off Beel from Oga to achieve the exact same effect, all the while making it look like he was aiding the enemy. The second one of the spellmasters says it'd be enough power to beat Takamiya and Lucifer, Himekawa breaks the machine.
Chick Magnet: Oga, for some reason, seems to be attracting a lot of girls, at least one of whom is definitely in love with him.
Himekawa with his hair down draws a huge gang of St. Ishiyama girls to their classroom to swoon over him.
Class Trip: After a lot of fuss the delinquents get to go along on a field trip to Okinawa.
Also Tojo as well. Even Oga thinks he's weird. He attempted to trade a little girl some guy was holding hostage for a box of candy.
Although the joke was that the candy, Chinsuko from Okinawa, sounds similar to the Japanese word for "penis", so the guy holding the hostage thought he wanted to... you know... trade the girl for his penis.
The Demon King is possibly even more random than both Oga and Tojo.
Being one seems to be a requirement for any absolute Bad Ass. Note how the three examples here are also considered to be the strongest in the story.
Comically Missing the Point: Kanzaki tells Futaba that Santa's dead in the hope that she'll give up asking for presents. Instead, she immediately comes to the conclusion that Santa is screwing around with her because she's a kid and goes on the warpath.
In Chapter 206, Mr. Saotome warns Oga not to fight Takamiya and Fuji as they are "worlds above" him. Cue Oga jumping to the conclusion that they're aliens. Saotome then tries to pound the fact through his thick skull by drawing a diagram... only for Oga to misread that too.
Ogadoes this a lot. When the truck that he's trying to hitch a ride from gets held up by armed robbers, he immediately assumes that they're asking for a lift, and starts worrying about how they're all going to fit.
Combat Commentator: Utterly skewered. When Oga starts calling attacks which are perfectly normal punches and kicks, Furuichi immediately starts making up bullshit to explain to the other people on the sidelines.
Later, during the volleyball match, one of the two official commentators is wearing a cat costume, and is only allowed to say "meow". Whenever he tries giving genuine commentary, he is chastised by the other commentator.
Comedic Sociopathy: Pretty much everybody on the series has sociopathic tendencies - even characters who are not supposed to be delinquents. Like 1-year-old toddlers.
Due to the manga's sudden cancellation (justified by its poor ratings the last several months), the final chapters was forced to rush the section of the Ishiyama Upstart arc it was on to end the fight against Fuji, and then capped the manga off with a 2-year-jump epilogue in the final chapter.
The same applies to the anime adaptation which rushed through the climax of the Akuma Academy arc to create a Gecko Ending.