Calling Stations (Being One and Playing Against One)

I've logged quite a few hours the last few days, and I've run across some difficult situations against calling situations. Here's one I was trying to figure out last night:

A bad player limps UTG. I have JTo one off the button and limp too (maybe not the best move, as we'll see). The button and SB fold and the bb checks. The flop comes:

K J 4 all offsuit.

Both players check to me. First level of thinking: what do I have? A middle pair with a medium kicker. Second level: what do they have? Well, the BB could have just about anything. The SB probably has some trash like A3 (he's that kind of player). So it seems entirely possible that I'm ahead here, and that if I bet someone is making a dubious call. I bet, the BB calls, and UTG folds.

Turn card: 4.

The BB checks again. What could he have? If he's holding a Kx hand (say K5 for the sake of discussion here) then I'm behind here - jacks up versus kings up. His call also suggests something like QTo, hardly worth a raise but worth a call with an open-ender to the nuts.

Does the 4 help him? Probably. Does it help me? Not particularly. But with a check to me, I'm betting it. If I get raised I'll throw this away in a second. He calls me again.

River card: 10.

There is no flush on the board. It's possible he rivered some weird straight like Q9 but I don't think so. I have jacks and tens, and he (probably) has kings and fours. There's a small chance that a bet makes him fold here, but this is low-stakes - he's not folding the river with a pair. So I check behind.

And our friend and adversary turns over 94 offsuit and takes down the pot with three-of-a-kind.

There doesn't seem to be a reliable way to get information from calling stations. They just won't bet or raise a hand. I should note one exception - if this player held an ace and hit a pair on the flop, he would bet. But other than that, he will not bet a hand, not matter how big. So without the nuts, I can't figure out what to do: if I bet I'll just get called, with no information about how to proceed on the next street.

Now today I got in a similar pickle. I hold KQo on the button and raise.

Flop: 7s 8s Qh.

Fantastic, just what we were looking for. The first player checks, the limper bets and I raise. The first player cold-calls (hmm) and the limper calls. The turn bricks. They check it to me and I bet. Both call. The river also bricks and we all check. I must win here with top pair, right? They were on flush and straight draws and missed.

The initial bettor turns over AQ of spades and takes the pot. He had top pair, top kicker, and a four-flush draw to the cinch hand since the flop. And he check-called all the way.

I know that "calling stations" are the people we want to play against, and we want to be tight-aggressive, and all that advice-book mantra. But calling stations can be extremely confusing because they will effectively "slowplay" monster hand and trick you (unintentionally, most of the time) into betting with a second-best hand and reading their calls as weakness.