I agree with Sarah and Ria, it's a dialectical difference. Plus, the more crass a subject is, the more words/euphemisms we use for it. ;)
As an Aussie, I'd use backside, bum, arse or clacker (my fav, very "educated" Australian, heh), but not tush, heinie, ass or butt - other people would use those.
As for "me" it's ease of pronunciation. I think "m-ee" is much easier to say than the grammatically correct "m-a-i". So you'll sometimes hear "me" said in place of "my": me mates, me car, me beer...