Jason's idea is excellent for security. The only drawback is one would have to have access to the stud in order to get the carriage bolt nut on. That may require cutting through the walls.
Another fix if the toothpicks do not work is to pick up a piece of wood doweling about 1/4" to 3/8" diameter. Drill a out the stripped hole with the exact same sized drill as the dowel. Use wood glue on the dowel and plug the hole. It should be a tight fit. Trim the excess doweling off so it is flush with the door frame. Once the glue is dry, the frame will be as good as new wood for reinstalling the hinge.