Body Horror: His left hand in itself. Specially when he loses control of it and Baki's powers almost consumes him. Hiroshi, Kyouko and Tamamo have to Time Travel to the origin of the Oni Hand to figure out a way to save him in the present.
Bunny-Ears Lawyer: He's goofy, friendly, outgoing and extremely silly. But he's a very good educator (both in the classroom, in Phys. Ed., and in field trips,) devotes his life and health to his students, and is so knowledgeable about the spirit world that people travel from afar to seek his advice. Oh, and there's the whole "badass exorcist with supernatural powers" part, too.
Chivalrous Pervert: He lusts over Ritsuko and more than one pretty lady, but never over his students and women younger than he is. In fact, he rejects Yukime's affections because of their nine-years age difference, and lectures Izuna when he thinks she's into Enjo Kosai. And while he's undeniably attracted to good-looking women, he keeps himself firmly in check and upholds his devotion to Ritsuko or to Yukime, when they finally become a couple, and he all but stops ogling women after that point.
Determinator: He will never give up when his students are in danger.
Parental Abandonment: His mother died when he was young. His father's disillusionment with people (he was the resident exorcist and helped everyone with generosity; they refused to help when his wife fell ill) caused him to grow cold and hardened and he abandoned his son while he sought fame and power.
Perpetual Poverty: So much that once he was haunted by Binbougami, the god of poverty.
It's also mentioned that he could make a great living if he used his Demon Hand for his own purposes; however, he willingly forfeits it because he wants to give a good example to his students and likely to not follow Jikuu's example. At most, Nube uses said hand to rig the local pachinko machines — since kids under 18 aren't admitted in pachinko parlors, they can't see him cheating.
Red Left Hand: And it's actually red —oni look, on the surface, like muscle tissue and grayish purple sinew.
New Transfer Student: The first official chapter of the manga. The first pilot ("Hell Teacher Nubo") had him as a regular student, but the anime took its plot and made him a transfer student again.
Parents as People: His dad is almost never seen since he works as a truck driver and often has to go outside Tokyo, but Hiroshi does care for him. His mother died when he was less than five years old, as said above.
Sleeves Are for Wimps: His most frequent outfit is a t-shirt with the sleeves rolled all the way up to the shoulders.
Voiced by: Rumi Kasahara
A-Cup Angst: When you have Miki as your schoolgirl rival and close friend...
Apologetic Attacker: When she abducts and almost kills Ritsuko. She's doing it only after being mentally broken by Ippon Datara, so she apologizes all the way through it and repeteadly tells her victim things like "I'm so sorry", "it's not your fault", and "I wish there was another way to do things!".
Back from the Dead: After refusing to kill Ritsuko and being tortured to death by Ippon Datara, her body melts in snowflakes. Later she reappears, but with Trauma-Induced Amnesia and it takes quite the effort to give her her memories back. (And the manga implies that she never truly remembered everything in her past, but was happy to make a new life for Nuubee and herself.)
Heroic Sacrifice: To save little!Nuubee when he was first haunted by spirit-devouring youkai. Later, when she merges with Baki and assists Nuubee in sealing the Oni in his hand. It would take Nuubee YEARS to find a way to release her so she can properly die in peace.
Magic Skirt: Her skirt upholds her modesty despite its... almost non-existent length.
Sealed Good in a Can: The Oni Baki ate her soul when she was dragged to Hell. It came back to bite him when she manifested inside Baki while the later was about to kill an adult Nuubee, and thus she became the crux for sealing the oni in her former student's hand.
Sexy Mentor: To Nuubee, as she's a beautiful woman with a really nice figure.
Woman in White: She dresses in white. In the anime, only her blouse is white (her skirt is dark blue).
Cursed with Awesome: Playing around with astral projection turned her into a bona fide Rokurokubi: the "long-necked woman." While it frightened the hell out of her and her classmates when it first manifested (she feared Nube would kill her) now she thinks it's cool and has learned to use it to her advantage, from playing pranks on people to extending her neck across townwhich saved her life once, extending her neck so far into the air she couldn't hear the instant-kill cry of the mandragora.
Gag Boobs: They're so big they make her classmate Kyoko self-conscious about her own lack of endowment.
Gossipy Hen: While she loves gossip and info, she takes care to not hurt people too much about it. When her friends think that she leaked some very important secrets (which she didn't) and shun her, she almost has an Heroic BSOD and then goes searching for the culprit.
Hopeless Suitor: She has a very slight crush on Hiroshi, but it's rarely invoked. In a Bad Future chapter, she marries him, and gets very upset when Kyoko (who has skipped several years of her lifetime) cries over this revelation.
Jerk with a Heart of Gold: She's selfish and mischievous, right up to the point where she might hurt her friends. Once said friends are in danger, she does her best to help.
Ms. Exposition: She likes to keep up to date with yokai and obake, and is happy to frighten her schoolmates with the latest urban legend (the scarier the better.) Even Nube has tapped her for information on obscure entities (by pressing her head and clicking it like a buzzer.)
Friend to All Living Things: He actually loves animals and wants to be this. In fact, when he accidentally pisses off the spirit of an animal he once carelessly allowed to die, he offers his own life to appease it.
Butt Monkey: he never gets what he wants — something always happens to ruin any projects of his. This is a curse from a youkai, actually: Akira once almost died by drowning and said spirit wants to finish the work...
Ill Girl: So much that the Ayumi we see in the manga is a sort-of astral projection: she's permanently bedridden at home, but Nube taught her how to use her budding spiritual powers to create an image of herself that can go to school and have a normal education.
Kid with the Leash: An experienced trainer of kudagitsune, fox spirits that live in tubes (or pipes, or pens, or any kind of narrow cylinder.) She generally uses them for day-to-day tasks, but can also wield them offensively if needed, and was once chosen to care for a legendary kuda because of her skill raising them.
Miko: Defied since she left her shrine and family way too early.
Superpower Meltdown: When her pyrokinesis first manifests, Nube and the kids worry that she will lose control and literally melt from it. It almost happens.
Voiced by: Hitomi Oikawa
Aloof Dark-Haired Girl: She's tallest than the average sixth-grade girl, has long black hair, and doesn't interact lots with people. The other kids think she's beyond their reach and treat her like a princess, admiring her from afar but not approaching her.
Eyes Do Not Belong There: When she's possessed by a spirit that feeds on her anxiety upon both being a shoplifter and hating how the world sees her. At first it's just an eye on her hand, but soon they extend all over her.
Fan Disservice: As said above, the demonic eyes extend all over the body of a cute young girl.
I Just Want to Have Friends: Painfully aware of how everyone else thinks she's some unreachable Golden Girl, when in reality she desperately wishes to get close to others.
Aloof Ally: He hovers around Nube to discover the secret to his strength and occasionally helps out.
Badass Teacher: Despite only posing as an educator, he's still badass as one.
Becoming the Mask: He had initially intended to stay close to Nube to see what made him strong, and thus learn how to defeat him; eventually he became a legitimately good person who would fight to the death for Nube and his students.
Baleful Polymorph: Does this to the boys of the school when they piss her off beyond her limits... via transforming them into panties. How should the spell be broken? Via having the girls wear themAUGH!
Body Horror: What he does on the people of a nearby village towards the end of the manga.
Overprotective Dad: Yukime's. According to him, Yukime's mission is only to be a yuki onna and keep the natural balance of her home; when she fell for Nube and went to the city, she broke said balance.
Batman Gambit: He tells Yukime that, to finally earning her right for a normal life with Nube, she had to kill a beautiful woman (like Ritsuko). This was a lie: what he truly wanted was to mentally destroy her so she'd turn back into the cold yuki onna she used to be and he'd be able to take her back to the mountains.