The Morose Mononokean (Fukigen na Mononokean) is a really good one. I don't know if you've seen it already, but if you haven't, it's about a boy who gets roped into working for a teenage exorcist. The genres for it are supernatural and comedy.
Another good anime is Devils and Realist (Makai Ouji), which is a couple of years old, so I don't know if you've seen it already, but if you haven't, it's about a boy in high school who is a "realist" and doesn't believe in things that can't be explained by science, then a few demons come and say that he's the elector and he needs to elect a new leader for hell. The genres are supernatural, school, and comedy.
Handa-kun is also really good and funny. It's about a high school boy who is super popular, but since everyone is too afraid to approach him, he thinks that everyone hates him. The genres are school and comedy.
Servamp is one of my favorites, buuuut I dunno if you'd like it, but I definitely recommend trying it out. It's about a high school boy who picks up a stray cat off the street, which happens to be a vampire, and he accidentally makes a pact with him and they fight against an evil vampire named Tsubaki. The genres are supernatural and school.
One of the romance ones that I really like is Actually, I am..., which is about a high school boy who accidentally discovers that the girl he has a crush on is actually a vampire. He then goes on to meet a bunch of other monster girls at his school (alien, werewolf, ghost, etc). The genres are supernatural, school, and comedy.
ANOTHER really good one is Monthly Girls' Nozaki-kun, which is about a girl who confesses to her crush, but he thinks she's asking for an autograph, and he turns out to be a famous shoujo mangaka. The genres for this one are comedy and school (and sort of romance?).
So, last but not least is my absolute favorite anime, Hakata Tonkotsu Ramens. Again, I don't know if you'll like this one, because it's not really under any of the genres you like, but it's super good, so try it out if you want. It's about a group of hitmen, and it's a little violent, so if you're not into that, then I wouldn't suggest watching it. The genres are crime and tragedy (I think lol)
Also, a good k-drama movie that you might like is Midnight Runners, which is about two police academy cadets who go out to flirt with women, but end up witnessing a girl get kidnapped. (I suggest using DramaFever to watch it). The genres for this one are comedy and crime, I guess?
So sorry for rambling haha. I hope this at least helps a little!