Toilet leaks into the wall after the flushing stops?
This sounds like the float valve inside the toilet might be allowing the water to drain down the overflow tube.  Normally, the float will stop the water before it gets to the top of the overflow, but if the float is leaking or out of adjustment, the water can spill over the top.

When water leaks into the overflow, it goes into the tank, and when it goes into the tank, it fills to the point that water will start to trickle down the drain.  When the water trickles down the drain, you may be able to hear it "running" down the sewer pipe in the wall.

Take the lid off the toilet tank and watch what happens after you flush.  Any draining issues should be apparent.  The same thing can happen if the flapper valve is leaking, but then you normally hear the toilet fill back up a little bit every few minutes.