I think mark f just wiped out everything I was thinking of suggesting. I'll highlight some of those.
Love Exposure
A Page of Madness
Why Don't You Play in Hell?
Tampopo
Battles Without Honor and Humanity series
The Tale of Zatoichi
Youth of the Beast
I'm a fan of Sion Sono, but still haven't caught up to half his catalog, only slightly less prolific than Miike at the moment.
Play in Hell might turn you off for seeming to be an ultraviolent exercise, but in fact is a satire of ultraviolent nihilism (and I think Tarantino's
Kill Bill was its prime target, but I can't confirm that).
Page of Madness is a surrel silent film taken place in a mental asylum. It's plenty surreal already, but also, when it was rediscovered in the 70s, the old director had forgotten the order of the reels, so we've never seen it in its proper continuity. Still wildly evocative and hypnotic.
Tampopo is the best Japanese comedy of the 80s.
Battles is director Kenji Fukasaku's gritty crime drama, an excellent counterpart to its contemporary gritty police dramas of the American 70s, Italian poliziottesco, and also portends John Woo's later Hong Kong classics.
Even if they're samurai films, Zatoichi is such a sympathetic and compelling character that it might transcend it for you. Either
Tale or
Chest of Gold are good samples.
I'll try a novel suggestion and go with
Female Prisoner Scorpion. These might seem like exploitation on their surface, but, at least the first couple, definitely have an art-house vibe, and I'm sure you'll be won over by some of their more memorably bizarre images.
Who else? Naruse has been mentioned, as well as Oshima, but for the latter, I'd seek out whatever you can. An Imamura that hasn't been mentioned (I think, it's hard to keep up) would be
Profound Desires of the Gods. And among the J-horror, I might add
Audition and
Dark Water.