Here are a few bands that I think tend to be kinda weird. I’m omitting other-cultural stuff that may not be weird if you were more familiar with it. (I haven’t read most of the thread, so I’m sure there will be some duplicates.) This list is in no particular order.
Also, you might want to Google for “outsider music”.
Also check out the stock at Wall of Sound.
Pauline Oliveros: Heavily-distorted electronic accordion. I’m not especially fond of this, but it’s interesting.
Johnny Dowd: Tortured country noir.
Hawkwind: The definitive spacerock band. I suspect other people would think them weirder than I do, but any band that put out a live double album about Elric probably deserves a spot on the list.
Robert Calvert: The mad poet of Hawkwind. Had a thing for concept albums.
Throbbing Gristle: They invented industrial music.
Chrome: More early industrial. Get into an altered state of consciousness and play it loud. The aural equivalent of an ice pick slowly driven into your skull…in a good way. See also Helios Creed.
Coil: An offshoot of Throbbing Gristle (along with Psychic TV). See also Black Sun Productions.
The Damo Suzuki Network: The vocalist from Can channelling the spirit of the universe. With the boys from Pressurehed and Farflung serving as backing musicians.
The Residents: Too much variety and weirdness to describe in a single bullet point.
The Trachtenberg Family Slide Show Players: They’d buy boxes of old slides at yard sales, then make up songs about them. Managers’ meetings at the McDonalds Corporation never sounded so good before.
The Blood Brothers: Post-hardcore.
Modest Mouse: The early stuff, anyway.
Im Silo: This was a one-off binaural recording of mellow-ish music done in a big silo. Even at low volume, the reverberations make you queasy.
A Midnite Choir: I don’t think this band was weird, but other folks might. Imagine the unholy offspring of Tom Waits and Spike Jones. See also Circus Contraption.
Is ambient dark electronica considered weird? There are a whoooole lot of bands doing that.