I have never heard it with the preposition. I think this is US only.
kinai: Piss is not only vulgar, it's a swear word, about as strong as 'shit', so be careful when you say "piss yourself". To give you an idea, it would not be used in a network sitcom (like Big Bang Theory, for example).
Hmm, no we don't say "wet on himself" in the US either. Actually I had thought it might be a UK thing, but I guess not.
Yes, "piss" is vulgar, and wouldn't usually be said on network TV, but I wouldn't say it's as strong as "shit". For example, I can't imagine it being censored or bleeped out, while "shit" certainly would. That's just in my experience, though.
I googled "wet on himself" and a few dozen pages came up. It seems to be used by some people when talking about their dogs' incontinence, and there's a few instances of people using it to describe their kids' wetting themselves. I think it's just an instance of a minority looking for a way to distance the word from the reality.
Interesting, I don't think I've ever heard it said that way. It's not something I'd say myself. For me, the most common euphemism for that would be "he had an accident", though that can refer to other bodily functions too.
Kinai, remember that pee is just the phonetic rendering of the letter P, which in this case stands for piss. So pee was originally used as a euphemism for piss, which is considered a vulgar word. It's like saying "the F-word" instead of fuck.
Therefore, any construction that can be used with piss can also be used with pee, and vice versa.