emily People do use "pissed" in the UK as short for "pissed off", but you're right, it is more commonly used to describe inebriated. However it's becoming more popular. Laziness?!
Saying someone is pissed as in drunk is considered mild to moderately offensive. I wouldn't say "he was pissed" in front of my granny but I would likely say it in conversation with my friends or siblings. It's more of word used in conversation with peers than anyone. Outside my social circle I would just use the word drunk.
"Piss off/pissed off" is swearing, but oddly,"Piss off" with a smile in response to a statement can be (in some unique situations) affectionate or funny. Affectionate: Friend 1: "Have you lost weight? you look great". Friend 2: "Piss off". However this doesn't mean, piss off. It means "I have lost a few pounds, thanks for noticing". It's a kind of shy modesty disguised as an insult.
Funny: If two people have had a heated debate about something, one might break the atmosphere by offering a brew. Other person might say "piss off" with a smile. This means "go ahead and brew up, it's a truce". But "piss off" without a smile means, get lost.
I find it fascinating too 