+1 As a few of the previous posts have stated there is something wrong if all your batteries in the ST have died in a week.What's connected to it? with nothing connected to the outlet you shouldn't have any draw from it. So, unplugging whatever is plugged in should also "solve" the problem.
In disconnecting the outlet you may have found the what but not the why. Either the outlet has some damage in the from of a short or it was connected incorrectly or the wires connecting it are damaged. A typical outlet/socket should have no drain whatsoever if there's nothing plugged into it. Is the socket connected to a relay? (Mea culpa I haven't read the whole thread.)
Here's hoping you find out why disconnecting the outlet has stopped the drain.