Ruins: Extremely progressive rock/zeuhl, genius-level drummer (not exaggerating).
OOIOO: Similar in some respects to Boredoms, but more upbeat and calm. Dreamlike, even.
Boredoms: Completely goddamned insane if you listen to their first couple of albums (Pop Tatari, Chocolate Synthesizer), and weird/tribal if you listen to their later albums (Super Ae, Vision Creation Newsun). To be honest, I prefer their older work, but both are good.
Melt-Banana: Is it punk or noise rock? Does it matter? It's hard as all fuck, and feels like pure victory in music form. Features one of the most underrated guitarists around.
Deerhoof: Catchy, clever melodies and an upbeat style. This is probably the most accessible band in this list.
Ni-Hao!: There are a lot of bands with this name. I am referring to the one from Kyoto. Their 2005 album Gorgeous is perfect. They take a simple style (two bass guitars and a drum kit) and breathe so much life, creativity and fun into it that I'm very happy they made an album. If only they'd made more..
Afrirampo: Surreal. At first their music can sound a little chaotic, but there's a method to it. These are very talented musicians, so don't let the fact that they're yelling "I AM BIRD" put you off.
Koenjihyakkei: Has the drummer from Ruins, maybe a little less experimental than that band, but it makes up for it with extravagance. Operatic vocals, lots and lots of instruments, the same made-up language. Always worth a shot.
Nisennenmondai: If you listen to Destination Tokyo you may get the impression that they're strictly a kraut-rock kind of band. I think this is a misconception, after seeing them live it becomes clear that the right way to play their music is loud and maybe even with the bass turned up. Hypnotic and fascinating.
eX-Girl: Surreal, surreal, surreal. Experimental and very catchy songs about being from a frog planet, a war between vegetables, a gas lady and so on. Also very, very good. Well-composed and well-played.
These all fit into your request for rock.