Humans: Mundane human beings living in the town of Sorami, somewhere in Japan. They are blissfully unaware of the presence of Synapse hanging over their heads (save for one guy)... until the Angeloids made their presence known.
The local pervert and (therefore) all-around Unlucky Everydude. Lived alone in his home in Sorami Town until the Angeloids showed up.
Chronic Hero Syndrome: Doesn't matter if an Angeloid can kill a human just as easy as snapping a twig. If saving a friend means putting himself in danger, he'll do it. Astrea even lampshades this by saying that's why he can't learn about Chaos. If he did, he'd put himself in a dangerous situation again. Could also count as his Fatal Flaw, as that's what gets him killed in Chapter 71.
Determinator: It doesn't matter if it's a perverted cause or a heroic one, Tomoki will see it through.
Jerk with a Heart of Gold: Tomoki is a true friend who would do anything and sacrifice everything for the people he cares about. He would do only marginally less for perfect strangers who he's just met. He is also a pervert of such high caliber that his perverted antics, though Played for Laughs, sometimes cross into sexual assault.
Here's an interesting example, when he and Sohara were "stranded" on an island for months, they were relatively happy with each other, despite the threat of being there forever. Tomoki even curbed his perversion completely just to take care of her! When the opportunity arose to take things... further, he was actually hesitant. Seriously, he accidentally touched her breasts and everything and he was nervous (no chibi mode in sight, either!). He may be the town's biggest pervert and loathed and hated by every single girl outside his harem because of it, but when it's time to be serious about affection and intimacy, he's serious.
The Peeping Tom: Tomoki takes it to the extreme by having Ikaros stop time while he gallivants around the city, stripping down high school girls all around. He actually shrinks himself and sticks himself in the cleavage of another girl.
Perversion Before Reason: His first concern (when it comes up) is helping out his friends. His second, and by far his most prominent, is his perversion. Anything else, including self-preservation, comes a distant third.
Lethal Chef: in the manga, it's her sunny side up eggs (see chapter 41).
Tomoki: Eggs are... a symbol of existence. No... They are life itself. And so... these sunny side up eggs. (Pokes one with his fork causing a demonic spirits like odor shooting out scaring Astraea) SEE! It's a scent of death!
Mr. Exposition: He usually gives a history lesson which usually has some relevance to that episode's plot.
Only Sane Man: Sometimes he's the only one who doesn't overreact to everything going on.
Take a Third Option: Despite sincerely wanting a new world, he was able to provide Tomoki with a way to reset things.
The Unfavourite: BIG TIME. Apparently, he and his big brother were pretty tight when he was a little kid; they'd make all kinds of planes, big and small, to send into the sky. One day, though, they got into a pretty pointless argument. His brother shrugged it off immediately, but Eishiro was still angry. Therefore, he half-assed his inspection of their latest glider out of spite. Naturally, of all days for something to go wrong, it had to be then...and it got him killed. When their parents found out it was his fault, they quickly learned to hate him, and when his baby brother was born, Eishiro was all but disowned...and they will never forgive him. There is a reason why talking about his family is such a sensitive subject, and why he wanted a new world so damn badly.
Token Evil Teammate: She often performs this role to get things she wants done, such as forcing Tomoki to join the New World Discovery club largely against his will. She also sponsors a gun shooting contest using very realistic looking toy guns, as well as a boys vs girls snowball fight, and a wrestling tournament in which she tries to punish Tomoki, and oddly enough, Sugata.
A Shrinking Violet farm-girl that develops a crush on Tomoki from overseeing his antics throughout the series. She later joins the New World Discovery Club to get closer to him and the rest of the main cast. She is later erased due to being hit by a truck, but is resurrected as the Angeloid, Zeta.
Early-Bird Cameo: In Forte. She appeared once in episode 5 and once in episode 12. The central plot of the movie is her arc in the manga. She also appears for a split second in episode 4 of Forte during the snowball fight.
Cultured Badass: He's quite skilled with a violin, and is a lover of orchestras... And is not afraid of driving into the household of one of Sorami's richest families with a firetruck followed by dishing out some verbal asskicking, calling out said family on their treatment of their elder son.
Later on, he ups this by tanking an assault from Ikaros Melan to buy some time to Sugata.
Iron Butt Monkey: If you can come out of this like nothing has happened, then you certainly qualify.
Jerk with a Heart of Gold: He's arrogant, condescending, and all in all a bit of a prick. He's also a good friend and when it comes down to it, he knows what's right and what's wrong and will unflinchingly do what's right.
Meaningful Name: In Chapter 76 she lives up to her name, as her wings catch on fire and burn up while she is carrying Tomoki in midair. It's stated this was a self-destruction system put in place in case she ever got too close to Synapse without permission.
Multicolored Hair: Her side bangs along with her messy hair and that innocent face of hers increases Ikaros's cuteness level by over 9000!!
Named Weapons: She has the most so far. Artemis, Apollon (her bow, whose power is said to be enough to annihilate a country), Aegis, and Hephaestus. The anime gave her one more weapon, Uranus System, a giant cloaked battleship/Mobile Armor.
A-Cup Angst: Made worse by the fact that her Love Interest is a devout fan of breasts and she will be eternally flat according to her age device. For extra measure, she's also the only flat-chested character in the entire series. Even Chaos' grows a bit as Forte and Chapter 70 shows. Even the background female characters have a bigger chest.
Big Eater: Ate four pieces of cake in chapter 60 — her's, Astraea's, Ikaros's, and Tomoki's.
Covert Pervert: Judging by how willing she is to watch pornographic movies with Tomoki and let him do perverted things. She also has very explicit daydreams when she sees Tomoki do perverted things.
Crippling Overspecialization: As noted by the Master, there's not much use for an electronic warfare type against underdeveloped downers. She's quite effective against Synapse's own tech, once Nymph evolves her abilities a bit, as shown in chapter 55 when she completely decimates an army of higher powered, more advanced Angeloids.
Named Weapons: Super Pyrotechnic Compression Firing Cannon, Prometheus.
They also both have S. vibrate claw Nemea.
Shameless Fanservice Girl: The oldest doesn't see any shame in wearing all the Fetish costumes Tomoki picks out. Until he picks up a bikini. She's absolutely mortified to see a piece of clothing that exposes her bellybutton.
The Ditz: Oh, God. Calling her a moron would be the understatement of the year. She can't even figure out basic addition, and she managed to fall behind in every subject on only her first day of school.
Ikaros: "You have three apples and four oranges. How many total pieces of-"
Astraea: "I eat all of them!"
Ikaros: "Ok, let's move on. Seven bananas-"
Astraea: "I EAT ALL OF THEM!"
Genius Ditz: She's actually fairly clever (Of course, being an idiot, she nearly always misapplies this, leading to a lot of Rube Goldberg plots that don't actually work).
Dumb Is Good: She's a complete airhead and one of the nicest characters in the series.
Dumb Muscle: She's exceptionally stupid, but she's also exceptionally strong. She's also the only angeloid shown to be strong enough to break her own chain. For comparison, breaking Nymph's chain took the combined efforts of Tomoki, Sohara, Miyako, and Sugata.
Friendly Enemy: Before she broke her chain, she was extremely friendly with the main cast. So friendly, in fact, that her switching sides can't even really be called a Heel-Face Turn.
Kick the Dog: An accidental case. She mocks Nymph for having no wings, trying to simply Poke the Poodle and not realizing beforehand how sensitive a subject it was. However she immediately regrets it afterwards upon seeing how hurt Nymph was.
Lightning Bruiser: She is the strongest and most agile of the first-generation Angeloids. She loses to Ikaros in terms of raw balls out speed, however, but in battle, where agility is just as important as speed, Astraea comes out superior.
Sacrificed Basic Skill for Awesome Training: Well, not "training" per se, but rather the details of her design: she was given overwhelming power at the expense of her intelligence. In other words, her incredible strength and speed in combat is offset by the fact that she's too dumb to even feed herself. In one instance, while fishing, she tries to eat the bait instead of using it to catch fish.
Chapter 75 is the worst instance of this, with her voluntarily sacrificing herself just so Chaos wouldn't die alone.
Training Montage: She had one during the credits of the fourth episode in Forte.
Unskilled, but Strong: According to Daedalus: "The reason I didn't add any processing capabilities to Delta... is because she doesn't need any." Astraea does note at one point that she's no match for Ikaros in a straight fight because Ikaros has skill and tactical acumen while Astraea only knows how to hit things really hard.
The first of the second-generation Angeloids, and also sent to Sorami City to kill Tomoki. Looks can be totally deceiving with her. Her formal designation is simply Second-Generation Angeloid, Type Epsilon.
Love Freak: One of the most blatant examples in all of Manga and Anime. Even her character song is named "Ai wo Ageru", i.e. "I'll give you love". She doesn't know what love is, though, but that doesn't stop her from being a freak about it.
Named Weapons: Not a weapon per se, but she had the Pandora System, which enables her to evolve her capabilities.
She also have Medusa and Chimeraas well as stronger versions of Ikaros, Nymph and Astrea's weapons.
No Sense of Humor: Tragic example. The reason she killed Hiyori in the first place was because she walked in on Tomoki's skit of chasing the Angeloids out of his house and took it seriously.
Omnicidal Maniac: What makes it so heart wrenching, is that Chaos doesn't want to be the walking instrument of death and destruction she has become. Chaos wants to experience genuine love, but due to the means of her creation and various story events, she is truly unaware of how to interact with others without causing pain and murder. When Tomoki gives her the opportunity to experience loving compassion first hand, he becomes the bedrock of what little sanity she has left. After this event, Chaos' grabs for power are nothing more than an attempt to experience Tomoki's kindness again, yet ironically they further distance her from achiving that goal.
Plot Driving Secret: In the manga, Tomoki remains ignorant that Chaos is an Angeloid. He only knows her as an innocent little girl, and not an insane weapon of mass destruction. Her battles against the other Angeloids has always been either away from Tomoki or while he's knocked out.
Winged Humanoid: Comes with being an Angeloid, however, her wings have more of a fin-like design to them to go with the mermaid design.
A generic medical specialist Angeloid who follows Sugata back from a dive game.
Jerkass: Because Mikako was the one who gave her the ability to speak, she is this to Nymph because she used to routinely bully Oregano and her sisters back in Synapse. By forcing them to listen to her sing.
Synapse: A few floating islands in the sky, which happens to stop over Sorami town at the time being. Their denizens are Winged Humanoid race called Angels, and they possessed vastly advanced technology compared to humanity.
Master of Synapse/Minos
The aptly named ruler of Synapse. Has a deep disdain for humanity, and creates Angeloids as his playthings... well, humans are too, by extension.