Barring a supernatural being using X10 to get your attention
I have to admit, when the lights came on in the middle of the night and then came on again five minutes after I turned them off, this thought definitely entered my mind!
To answer some of your questions:
Nope, no new CFL bulbs in the house.
I used the controller to turn the lights on and off while my husband stood in the window and watched the neighbors' houses, but we couldn't see any of their lights flash on or off. That would be sort of fun, though!
The lights do come on by themselves even when the controller is unplugged.
The ceiling fan in the bedroom doesn't have lights. The wall switch for the fan is a simple on/off switch; no dimmer.
Here's what I found when I removed the plates: the lights in the kitchen were set to A1, and the lights in the bedroom were on A9. (There are similar switches in two other rooms in the house, but these are the only rooms where the lights come on by themselves.) I moved these to B1 and B9, respectively. I checked behind the ceiling fan switch while I was there, and found it attached to a module labeled "Master Wall Switch Module with A.G.C. for single and 3-way applications/Model XPS3."
The Powerhouse controller is set to "A" in the top right corner, and when I try to turn the lights on or off now, using the controller, the kitchen and bedroom lights don't respond but the ceiling fan does. I guess the ceiling fan is still set to A?
As I was standing in the kitchen writing down some of these numbers, the lights switched on again by themselves. Normally this happens when I'm not in the room, so I'm pretty sure it's mocking me at this point.
Thanks again for helping me with this!