Piss = I need to take a piss = I need to go and relieve myself
Pissed = I'm really pissed = I'm really drunk
Pissing = It's pissing it down = It's raining really hard

In general, X'ed Off means annoyed, vis:

Pissed Off = I'm really pissed off/that really pissed her off = I'm really annoyed/that really annoyed her.

As Tony says, "piss off" means "get lost". Again, in general "X off" means "get lost".