I would never play trips this conservatively in a tournement, all you can do now is shove, nad hope they have a K,7,PP.

With your check on the flop, the turn is where you get the money in here... you missed your chance by the river, I'm afraid.

With a bet and a call, at least one of them has a 7 and expects to split with another 7. They aren't going to put you on QQ-AA since you didn't raise preflop and didn't bet the flop. Maybe they should be scared of 88-TT, but how many players are that smart? As for your actual hand, people just don't generally think quads are realistically possible. Most people assume any 7 is pretty much teh nutz on that turn. If they both checked the turn, then it would be different - probably neither had a 7 then, and you'd give them another chance to make a boat on the river, or best of all for you, a second 7.

With the bets on the turn, the K is bad for your hand, as neither of the other two players are likely to have one. You shouldn't have one either, unless it's K7, but again, how many players are smart enough to know that? They'll see it as a scare card and might fold now if you shove. Still, with those stacks, I think shove is all you can do and hope that at least one of them still thinks they're splitting with another 7.

Also, your description of the flop is inconsistent with your description of pre-flop. You say the other two players are EP and MP and you're LP, but then you say that you checked and then they both checked. If you were out of position with a J here, I would probably check-raise it... but as last to act, when they both check to you (which is what actually happened, if you're remembering preflop correctly), I think you should bet, as it will look like a steal, and you'll get called by a 7, a pocket pair, and maybe something like AQ thinking you're full of it or just have a 7, and hoping to resteal on the river if you look weak on the turn.

That last bit, incidentally, is why I find that bet-check-bet is a much better trapping pattern than the usual check-bet-bet or check-check-bet slowplay. People have learned to be wary of the regular slowplay, whereas betting the flop, checking the turn and then betting the river really looks like a bluff to a lot of people, especially if both cards blanked.

P.S. 22Fish, I know that historically, any 3-of-a-kind was called a set... e.g. in Super System, Doyle Brunson talks about "a Set of Trips"... but I think that these days, most people reserve the term "set" for trips made with a pocket pair and one card on board, as that's an entirely different kind of hand from regular trips and played entirely differently, so we need different terms for them so we can keep them separate.

As an aside, here's an example of the bet-check-bet variation on the slowplay that I recommend using for trips (sometimes, against the right opponents, etc. all the usual caveats), at least heads up, or at a 6-max table when you get the flop heads up. I think the guy would have called me all the way to showdown with his ten, but I'm pretty sure he wouldn't have raised the river and given me an opportunity to get all the money in. I didn't know he had a T, though... when he raised the river, I figured him for AQ/KQ/QT or something of the sort. Point is, he might have raised that river even with no hand if he thought I was weak, but if I'd checked the flop and then started raising on the turn or river, it would have been a giveaway.

Seat 1: Xopods (1,965)
Seat 2: do it 23 (1,035)
do it 23 posts the small blind of 15
Xopods posts the big blind of 30
The button is in seat #2
*** HOLE CARDS ***
Dealt to Xopods [7c 3s]
do it 23 calls 15
Xopods checks
*** FLOP *** [7d 7s Tc]
Xopods bets 60
do it 23 calls 60
*** TURN *** [7d 7s Tc] [Qd]
Xopods checks
do it 23 bets 90
Xopods calls 90
*** RIVER *** [7d 7s Tc Qd] [2h]
Xopods bets 180
do it 23 raises to 540
Xopods raises to 1,785, and is all in
do it 23 calls 315, and is all in
Uncalled bet of 930 returned to Xopods
*** SHOW DOWN ***
Xopods shows [7c 3s] three of a kind, Sevens
do it 23 mucks [Td 6s] - two pair, Tens and Sevens