I just want to put a shoutout here to
Mawaru Penguin Drum, as long as the thread OP doesn't mind me doing so.
I feel that Penguin Drum had the misfortune of airing the same year that Madoka Magica and Steins;Gate did, and for that reason and others, I think it's sadly underrated and now rarely talked about it seems.
But I think its
particularly underrated as a comedy. There's probably no anime that aired in the past two years that made me laugh more than Penguin Drum did.
I guess of the categories listed in the OP, it would fit most neatly into "Absurd Comedy".
The anime show that made me laugh more than any other is probably
Excel Saga. Which also probably fits most neatly into "Absurd Comedy".
I guess I would say that Absurd Comedy is something that anime does particularly well.