First thing that comes to mind, are the tires/wheels also imported as Z-Up? Both need to be X-Axis positive (front of car pointing positive X) and Z-Up.
Although your vehicle’s root is at 0,0,0, the crazy physics seems to occur when the root bone (and wheel bones) have a rotation value that is not 0.0,0.0,0.0.
In 3dsMax the bone rotations are by default -90.0 on the Z axis, which is a problem when imported to UE4. For Maya however you will need to rotate each bone so that Z-up = 0,0,0 which should be -90x, 0y, 0z in Maya.