The pilot reported that, while landing on runway 24 at night, with a crosswind, the airplane veered to the right and despite his control inputs to correct, the airplane exited the runway onto the adjacent soft terrain. Concerned the airplane may “get stuck” in the soft terrain, he maintained power and continued to taxi towards the taxiway. He heard and felt a bang that jolted the airplane. After slowing and turning onto the taxiway, the airplane would not continue. After shutting down the engine, the pilot inspected the airplane and found that the right main landing gear tire was flat, and the left wing was substantially damaged as a result of a collision with a taxiway sign. The pilot reported that there were no mechanical failures or malfunctions with the airplane that would have precluded normal operation. The pilot reported that the automated weather at the time of the accident was reporting the wind from 290o at 12 knots, gusting to 24 knots.