Man, some of these bands mentioned are pretty conventional in terms of coherent song structures, predictable tonality, etc. Their looks are weird in many cases. Deerhoof is actually quite popular with hipsters and has gotten progressively less weird over the years. Milk Man was probably their high point of strangeness. They've become an actual good band since then. They're kind of the safe version of Melt Banana.
Dir En Grey has some really great material, and a listen to the albums really isn't that strange. Especially the likes of Kisou and Oroborous (despite the presence of a couple tracks like Domestic Fucker Family). Good band! Weird videos, though, I'll give you that.
Mr Bungle's "Disco Volante" has some pretty weird material on it, particularly the likes of "Violenza Domestica," though that one's...narrative. Mike Patton's "Adult Themes for Voice" was a good submission. Fantomas also has some strange releases. I think the first and third are the best (IIRC they were trying to represent comic panels). Most of these are kind of a successor to John Zorn's Naked City material, which was just trying to be as abrasive as possible.
Regardless of weirdness level, Mr Bungle - California is one of the best albums of all time. It genre hops like mad, though a few of the songs are straightforward genre recreations all the way through. It's brilliant. "Ars Moriendi" is likely the high point of strange, also the high point of awesome.
Bjork would be described as weird by most "normal" people, that's for sure, but she's so popular and I've listened to her for so long that I guess I'm fairly immune. Medulla would probably be the high point of weirdness. It's created entirely with (oft-manipulated) vocals. It's also probably my favorite album by her. The weirdest tracks might be "Where is the Line" and "Ancestors." It has some really catchy pop songs on it, too, but they're still quite odd sonically if you break them down. Ex, "Triumph of a Heart" and "Who Is It."
I love weird bands. Mr. Bungle is one of my favourites from the 90's era. I think some of these bands are pretty weird, too, but maybe my bar for weird is pretty high. When I posted this thread, I had not thought at all about bands that look weird but play mostly normal material.
If you guys haven't heard of Winny Puhh, I think they sound pretty weird, but their image is definitely weird:
Maybe this was weirder 5 years ago than it is today, though.