It's tough to nail it down to a particular genre. A few years ago I played in a 3-piece (guitar/vox, bass/keys/vox, drums) performing a few originals and a hell of a lot of covers (mostly R.E.M., Radiohead, Weezer type stuff). Since then, I've played with a couple different, more experimental, jam bands. One with a rotating lineup playing quasi-electronica with a hint of groove (think Disco Biscuits). The other group was another 3-piece (guitar, bass, drums) playing entirely improvised material. I like to throw these guys for a loop by picking an odd time (5/8, 13/8, 7/4, something fun like that) and switching in the middle of a groove, sometimes overlapping with the drummer's straight time until he catches on. There's video somewhere of one of our gigs, I'll try and get a hold of a copy.
As far as influences, I'd cite Brian Eno as my biggest musical inspiration. For bass technique, Jack Casady, Phil Lesh, and Mike Gordon are at the top of my list.
I wasn't able to get everything organized last night, but I will work on it tonight and tomorrow and will certainly keep you posted.
Adam