A couple of off-the -wall suggestions: During the daylight, turn off everything in the house or unplug it. Go check the power meter and see if it's recording any usage.

Is the house on a well? Could be a short to the well casing. Any close neighbors? They could be stealing power with a long miss-wired extension cord.

We had house with a basement in Portland. Part of the wiring that had been done in the basement ceiling had the hot and neutral reversed.

Does the house have metal siding? If so, could be source of AC, if not properly installed.

I know, these are all weird suggestions, but then so is the problem!

Paul