Evpok has it right with his comment: all is well explained in the article if you want the French definition of the term. To clear up things,
we can try some possible translations (I tried to vary on purpose but it’s quite arbitrary. Just giving an idea):
J’espère qu’elle va pas me souler.
I hope she won’t get on my nerves.
Arrête de me souler !
Stop pissing me off!
Putain tu me soules…
Damn, you’re boring me to death…
Je suis soulée.
I’m cheesed off with it. / I’m fed up with it. (pick your prefered version)
Ça me soule.
This really sucks.
souler quelqu’un means “to get someone drunk”. Se souler means “to get drunk”.
The other meaning which is much more frequent is “to piss someone off”.