I want to know who is the weirdest band you ever heard. I don't care if it's metal or rock or free-form jazz or avant-garde or no one knows.
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Metallica...
... just kidding. I'd say "Mr. Bungle" is weird while still being very musical. If the only parameter required is weird: consult youtube with search terms like "noise experimental atonal". You'll find material for years to come.