We had an issue along these lines some years back on our farm. We were getting VERY high electric bills. We checked and rechecked about everything, but still couldn't find out "where" that electricity was "going to." We even went away -- out of town -- with EVERYTHING turned off. We assumed that would prove that the bill could go way back down -- but by golly, we STILL got a high bill.
This went on for several years --- monthly electric bills of about $300, when it should have been about $60.
Eventually, one day I was out by the barn and saw a line of water coming in under the barn wall on one side. It was flowing under the concrete barn floor, and pooling up into a virtual flood in the field on the other side of the barn.
We used a backhoe to dig up all around the well head. Sure enough, about six feet down, there was a small crack in a fitting, which was PVC and not brass. ALL THAT TIME the well pump had been turning on and off 24 x 7, due to the leak. In fact, we had once replaced the well pump because it had died. Apparently the on/off running for years just burned it out.
We replaced the fitting for about $5, and never had a high electric again. I figured that we paid at least $200 a month for water running into a ditch, over the course of four years. We lost about $10,000 to that "little Problem."

I did contact the electric company, but they offered nothing to offset my losses.
You might also see if an outside night light (sodium or otherwise), could be drawing power.
I also was told by various experts that even if all your lights are off, freezer and fridge unplugged from the wall, etc, you will still darw a small current just to keep the service hooked up to the property.
Hakim