Fold the river you've really got no option with the one card straight + back door flush

As for the rest of your play...
Preflop its fine, just limping UTG with 7's
Post flop, it could be better... Raise to $3-$4 on the flop to get a better idea of what you are up against. If he called the raise you could put him on two pair/straight draw.

With the staright draw coming out on the flop + opening up a flush draw its really hard to know where you are with the reraise.

As for the river, I would have folded it all day long unless you have a great read.