The weirdest of them all was Sun Ra (60's and 70's era). If you are willing to move in a post-War classical music direction, then Stockhausen was the king of weird (Xenakis is pretty close). You might like John Cage as well.
For weird rock in the Zappa/Beefheart/Residents tradition, consider something like Bongwater.
More recent avante-rock like No Neck Blues Band or the Boredoms is pretty out there.
Here is a "ranked" list of top "Avante Garde" artists from allmusic guide:
1stThe Art Ensemble of Chicago60s-00sJazz
1stAlbert Ayler60s, 70sJazz
1stPeter Brötzmann60s-00sJazz
1stJohn Coltrane50s, 60sJazz
1stCharles Mingus40s-70sJazz
1stSun Ra40s-90sJazz
1stJohn Zorn70s-00s
2ndAMM60s-00s
2ndDerek Bailey60s-00sJazz
2ndAnthony Braxton60s-00sJazz
2ndWillem Breuker60s-00sJazz
2ndEugene Chadbourne70s-00s
2ndDon Cherry50s-90sJazz
2ndMarcel Duchamp10s, 50s, 60s
2ndMalachi Favors60s-00sJazz
2ndFred Frith60s-00s
2ndHenry Kaiser70s-00sRock
2nd The Kronos Quartet70s-00sClassical
2ndJoëlle Léandre80s-00s
2ndMisha Mengelberg60s-00sJazz
2ndRoscoe Mitchell60s-00sJazz
2ndMeredith Monk60s-00s
2ndWilliam Parker70s-00sJazz
2ndHarry Partch20s-70s
2ndThe Residents70s-00sRock
2ndMatthew Shipp70s-00sJazz
2ndDavid Tudor50s-90s
2ndOtomo Yoshihide70s-00s
3rd Aksak Maboul70s, 80sRock
3rdMaryanne Amacher70s-90s
3rdAmsterdam String Trio80s-00s
3rdJaap Blonk80s-00s
3rd Myles Boisen90s, 00sJazz
3rd Bill Brovold80s-00sRock
3rdHarold Budd60s-00s
3rdWilliam S. Burroughs50s-90sSpoken Word
3rd Rhys Chatham70s-90s
3rd Gene Coleman's Plus-Minus90sJazz
3rdLoren MazzaCane Connors70s-00s
3rd Tony Conrad60s, 70s, 90s
3rd John Corbett90s, 00s
3rd Michel F. Côté90s, 00s
3rd Alvin Curran60s-00s