Could it be someone who has (or had) access to the keys just messing with you as a prank? Does the varied state you find your car in rule out John's suggestion or confirm it?
Could it be that a bunch of teenagers want some place comfortable to sit & smoke and captured the signal from your remote? I'd expect them to leave some kind of evidence though and it seems odd that nothing has been stolen.
So, webcam is probably the best bet to find out which it is, and better to call the police than go out & engage an unknown number of miscreants (or your ex).