The main issue you'll have, if the cameras are separated by any distance, is parallax causing misalignment when stitching, particularly with nearby objects. There's also the fact that to cover a 360x180 spherical view reliably with enough overlap for stitching, you'd need a lens with a lot of scene coverage and even most rectangular 8mm fisheye lenses for APS-C aren't that wide (they're only 180º coverage diagonally across the frame, not along the edge). I've only ever been able to cover a sphere in four shots handheld with a full-frame circular fisheye. Theoretically, you can do it with two such lenses back to back, but that assumes you don't need any overlap for stitching or ghost/clone erasure.
It might actually be more practical to use a 360º camera (e.g., Ricoh Theta) mounted on the roof of the car, vs. four separate cameras and stitching, despite the lower resolution results.