Mothball,
Your plight is, indeed, a strange one. Has all the earmarks of a "B" teen horror movie with poltergeists, self opening doors, haunting moans and suspicious fogs banks roiling throughout the house.
But I don't dispute what your describing.
I had one last thought to at least nail down the presence or absence of a source medium: put a battery operated recorder or your cell phone into a, for instance, pressure cooker (or some other metallic container that presents a solid conductive "surround"), put it on a cushion and cover it with pillows to eliminate (or at least seriously reduce) RF/audio/vibration influences. Google "Faraday Cage".
Let us know what happens.
This will, hopefully, at least confirm/deny whether the noise is, or is not, purely electromagnetic.