What does a loud, rolling drumming sound coming from behind the wall of the bathroom sink mean? This noise was accompanied by knocking and vibrations. The water from the toilet also splashed up. No one was in the bathroom and no one had been using any water in the house at the time. Any ideas?

Turn off the toilet stop valve and see if noise continues. In the mean time tell what you mean by:

The water from the toilet also splashed up.

We didn't actually see the water splashing up, but when we stepped into the bathroom, there was quite a bit of water on the floor surrounding the toilet and on the toilet's open lid. We are assuming that some water - clear water - from the toilet must have shot up. There was also a very musky smell. It was very strange. The sound, also very strange, has since stopped, but we are wondering what caused it and if it can be prevented from occurring again. Thank you.

Remove tank lid and check that the little tube from the fill valve to the overflow pipe is in place. It should be attach to the top of the overflow pipe.

If water appears to have come from the bowl, that would indicate a possible blocked vent pipe. A blocked vent might force air out the sewer pipe through the toilet. That however would require water to have been used somewhere in the house.