The idiom "a pain in the ass" is considered as a vulgar idiom while "a pain in the neck" is the more "polite" version. Pity I can't think of more synonymic expressions/idioms.

I'd say it is vulgar, but also in common use. Go with "pain in the neck" or "pain in the behind". In Ireland you could say "pain in the áras", ie. replacing the vulgar word with an innocent Gaelic word (áras=hall), and another Australianism is "pain in the clacker".

"Pain in the neck" is the more polite way. Both are informal. "Pain in the ass" can be used among friends. I would not call it "vulgar", but would not use it at work or with my grandmother :)

nope!

It is the opposite. At least that's what I teach my students: "pain in the neck".