The student pilot reported that, while landing in a "strong" crosswind, the airplane touched down on the center line of the runway, but then veered hard to the left. He attempted to correct by using rudder and aileron inputs, but over corrected and the airplane veered sharply to the right and exited the runway. He applied full throttle to abort the landing; however, the airplane veered left across the runway, then continued off the left side of the runway. The airplane continued down an embankment, the nose impacted an "upslope" on the far side of a ditch and the airplane came to rest inverted. The airplane sustained substantial damage to the empennage and both wings. The student pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation. The automated weather observation system located about 1 mile from the accident site reported, about 15 minutes before the time of the accident, the wind was from 190° at 13 knots; and that about 15 minutes after the time of the accident, the wind was from 210° at 17 knots, gusting to 21 knots. The student pilot landed on runway 12R.