One time when I was still in middle school, I spent the night at a friend's house. Her dad suggested we should go up to a place called Gravity Hill. It was only a road and off the road, there was a slaughter house. After we drove up, the dad put his car in neutral and we faced up the hill. All of a sudden, we starting rolling and I was convinced the dad was joking and moving the car. But when I asked him, he pressed the gas and the engine reved but we kept rolling slowly.
After it ended, the dad drove back to where it started. But before he put the car in neutral, we got out and put baby powder all over the back of the car. Then we got back in and started rolling again. Thankfully it was really dark so we knew when another car was coming.
Then after the rolling stopped, we pulled over to the side and got out of the car. We took out flashlights and looked at the back. What I remember seeing was seriously creepy, there were shapes that looked like hand-prints over the powder. We ended up videotaping what we saw and went back home.
A few days later, I decided to look up where we went and the story behind that road was that there had been a school bus crash. Children died and the rumor was that the rolling was the children pushing the car to keep you from the same fate. Creepy Huh?
You mention gravity being messed up. Here is a possible physical (and very scary) reason for that:
Allisongabrielle pointed out that there are deep mines and "bottomless pits" in the area. Since gravity is caused by mass, such gigantic sinkholes would certainly affect the direction of gravity. If you're standing near the edge of a very large and deep sinkhole, then the direction of gravity will not be exactly vertical, but will rather point slightly away from the sinkhole. If this deviation in gravity is great enough, then cars will certainly roll in that direction. Even if it's slightly uphill. This is completely natural and physical and has nothing to do with the supernatural or paranormal.
The really scary thing about this is that it would take a mighty big sinkhole (or underground hollow region) to produce a gravitational deviation large enough to move a car. Not sure whether the mines/sinkholes that you already see are large enough, but if not, then there might be more and larger hollow regions underground that you don't see. These gigantic hollow regions could be enough to change the direction of gravity enough to move a car. If such a hollow region collapses, then people living over it will tumble down, down, down (perhaps miles or even tens or hundreds of miles) into the gigantic sinkhole. Yes, the natural/physical can sometimes be a lot more scary than the supernatural/paranormal!