After making a fuel stop on a cross-country flight, the pilot reported a left quartering headwind during the takeoff. He applied the proper crosswind control inputs and immediately after liftoff aligned the airplane into the wind to maintain a ground track over the runway centerline. The pilot reported a wind gust from the left impacted the airplane resulting in the left wing rising and the airplane banking to the right. Subsequently, the right wing, the empennage, and the right main landing gear touched down resulting in the airplane exiting the runway to the right. The airplane continued down an embankment impacting a chain link airport perimeter fence. The airplane came to rest upright. Examination of the airplane by a Federal Aviation Administration inspector revealed structural damage to left and right wings, the left landing gear assembly, fuselage, and empennage. The on-field weather station recorded the wind at the time of departure as 50 degrees left of the runway heading at 15 knots, gusting to 22 knots.