FTR isn't converting this hand properly so here goes:

I am in the BB w/ [Kc] 2 limpers, sb completes, I raise to $0.60, everyone calls.

Flop ($2.40) , ,
sb checks, Hero bets $2, UTG calls $2, other 2 fold

Turn ($6.40)
Villain has $5.20 left.

How do I deal with situations like this? Is it even possible for me to get away from this hand OOP?

What's beating you? Flopped sets, 7x, and AT. Sets got less likely with the board pairing, and if he really called a flop bet on that board with something like 87 then good for him, he's a moron and I'll get it back. Basically you're worried about AT and TT, while you're ahead of all sorts of club draws, straight draws, and AQ/AJ and even (at $10 NL) A9 and lower. I just push here and if he has me beat then oh well.

Why the hell do you wanna get away from it. I fist pump + bet!