Biffy Clyro, is definitely one of the strangest ones I've heard,
I believe, (although obviously I could be wrong) that their name originated when they were talking about Sir Cliff Richard,when the band was just forming, and they were a bit worse for drink, they were talking about 'Cliffy's' biro, (as in Sir Cliff Richard's pen)
because they had been drinking, their words came out wrong, and they found it really funny, that they had said' Biffy Clyro, instead of Cliffy's biro, so they decided that's what they were going to call their band!
I always thought Nuprin was a strange brand name. I couldn't figure out what Nuprin was supposed to be, since Nuprin isn't the name of the company, its just their brand of Aspirin. Things like Tylonel, have the name of the product as their company name as well. But then Nuprin was both unique in name and in product look. It was the first, and to my knowledge only, little yellow pill.
I always thought Motley Crue was a strange name for a band. Seems like these days the band names are becoming more unique and weird. eg Armor for Sleep, HIM, Matchbook Romance and others just to name a few.
Heh most of the bands I listen to have odd names... here are a few: Velvet Revolver, Mindless Self Indulgence, HIM, Panic! At the Disco, Breaking Benjamin, and The 69 Eyes.