UK
slang - bog, heads, jakes (but these are not very polite. There are worse names too but let's not go into those)
pretty everyday - loo, ladies, gents,
toilet - used a lot 20-odd years ago but starting to sound a bit coarse these days (and some people always found it awful)
W.C - lav/lavvy - I don't hear these at all but I've heard that lav is preferred in posher circles than those I move in! I could be wrong/outdated on that.
Bathroom - used sometimes in domestic settings. It sounds very silly to us to use it in contexts where there couldn't possibly be a bath/shower in the room, i.e in shopping centres. But actually I think this is increasing in use - an Americanism we are picking up.
Slang for going to use the bathroom
'going to see a man about a dog' (usually men)
'going to powder my nose' (women)
'going to/need to spend a penny (women)
These are not offensive, but are slangy (the dog one could be seen as rather coarse so watch the company when you use it). Again, there are some very coarse ones but I don't think you need to know those.