Live 4/8 hand. Missed opportunity?

[GreywolfNYC]

Live 4/8 game in NYC. UTG is a young Asian guy who seems okay but who is definitely on tilt. His hands have been getting cracked all night long. MP is a 2+2er and a very good player. LP is a loose, calling station.
I'm in the BB when UTG posts a live straddle. I'm dealt 7h9h.
MP calls the two bets, as does the player to her left, and the LP player. I call the extra bet and now UTG raises. We all call and on one hand I'm thinking, "Now we've got a nice multiway pot for three bets" and, on the other, "What am I doing here with this stupid hand?" Four of us see the flop.
3 6 8 rainbow.
UTG is reaching for his chips and I check. UTG bets, we all call.
Turn: 10
I start reaching for chips and UTG bets out of turn. I say, "Wait a sec, I haven't acted yet." I bet and everyone calls.
River: J
I lead, UTG calls with a sigh, 2+2er folds, guy to her left folds, LP calls. MHIG.
On the flop I could have led out. I could have checkraised. Who does which and why?
Did I miss an opportunity to checkraise the turn? Or was my line the right one? Comments please.