Do I say:
Hook me up to this nice party!
Hook me up on this nice party!
I am trying to give a connotation that the party sounds good and I want my friend to give me an invitation to go there. Should I say in some other better way?
Normally I think you'd just say "Hook me up!", but if you want to be more explicit, you can say "Hook me up with __!" (But I think "Hook me up with an invite!" is more natural than "Hook me up with the party!")
Neither of your constructions is fluent. The idiom "Hook me up" should either be used as a complete idiom by itself or to request means such as "hook me up with a ticket" or "hook me up with an invite."
Your first sentence:
would if it means anything mean that you want to be connected to the party like a wire to a stereo or electrical outlet.
Your second sentence:
seems meaningless to me.
It doesn't sound right either way. It's like you're trying too hard to be hip.
Better to say, "May I go to your party?" Or, "Please, invite me to your party!"