I've had good luck using a combination wrench. With the box-end on the bolt, I smack the opposite end with a big hammer. The shock will usually overcome the initial friction and get it started. Then I switch to a 3/8 drive ratchet / socket to finish removing it.
So, with the bolt head trashed, it will be a challenge. Can you get vice-grips on it? If so, try the hammer trick. If not, you need to decide if your tool arsenal is adequate to be able to complete the job. Don't get to the point of no return and end up getting the car towed.
Experience is something you don't get until just after you need it.