As a qualified electrician here in the UK, there are certain instances that can cause lights to turn themselves on depending on the switching style, wiring, etc. It may be worth maintenance having a look at them (if not done so already), if not just to rule out any possible natural explanations for this occurrence.
As for the mud, that is kinda weird. It reminds me somewhat of the manifestation of water at 30 East Drive, Pontefract ( the "Black Monk House") within the kitchen area. This has been put down to poltergeist activity within the property.
I agree with Lynne, if you are going to get to the bottom of this, whether a prank or otherwise, I would consider putting in some cameras covering the areas with the most activity.