'Classical' music has had the largest influence on me, but it's not what you'd call strange... Hmm. This is a hard one.
I've always been pretty eclectic in what I like listening to.

For classical music, I'd have to say that the strangest stuff I've ever heard is Nancy Telford's 'random music' (don't know what else to call it) choral arrangement of She's Like The Swallow. There were several sections where the choir each individually sang different phrases of text on three different notes, at random tempos, and the conductor merely decided when we all would move to our next notes. It's really hard to describe.
Sort of like the crowd noise when people are waiting for the lights to go out in the theater, and everybody's talking at once, only this had some musical structure added to it. Really strange.

That experience certainly influenced my creativity when I'm writing music. The thought that music doesn't have to be nailed down to an absolute time or even note is a liberating concept during the writing stage. For me anyway.
Eventually I do nail it down, but the concept of not nailing it down is an amazing one.
So, what's your strangest musical influence?

~*sirepseh*~