Primus
"Psychedelic polka" is how vocalist/bassist Les Claypool once described his band's sound, although "alternative funk metal with goofy lyrics and oddball melodies" is probably more accurate. Whatever you call it, it's extremely weird, but certainly not through any lack of musical skill - Claypool's talents as a bassist are legendary, and he once auditioned to replace Metallica's bassist in the Eighties. If you've ever seen South Park then you'll have heard one of the band's more accessible moments - they were hand-picked by fans Trey Parker and Matt Stone to write the title music. Best summarised by Claypool himself when he sings: "I am the Antipop / I'll run against the grain 'til the day I drop" (The Antipop).
Weirdest track: Grandad's Little Ditty