The pilot was returning to his home airport after a short trip. Other than mild turbulence, there was nothing eventful about the trip. Upon nearing the airport and listening to the weather, he understood that winds were gusting from the northwest at 12 to 20 knots. This was on the high end of his personal minimums, but within the tolerance range that he had flown in the past. As he was preparing to land, he experienced some greater turbulence and crosswinds. The air traffic controller in the control tower gave him a straight in approach, and subsequently cleared him to land on runway 25. The approach was turbulent, and the plane was being bounced and pushed left intermittently. Due to the wind gust advisory, he landed with only 10° of flaps and about 10 knots more airspeed. His estimated speed over the threshold of the runway was about 70 knots. He stated that it was pretty gusty crossing the runway threshold. He landed the airplane and once the nosewheel was down, he started braking. Unexpectedly the plane moved to the left quickly. It seemed to him as though a large gust hit the airplane from the northwest side and pushed the airplane sharply to the left. He worked to counter the movement with right rudder but was unsuccessful in stopping the momentum. He nearly kept the airplane on the pavement, but the left tire just slipped off the edge of the runway. When the left tire contacted the newly sodded turf, combined with the recent heavy rain; the tire sunk quickly, as the turf was soft and very muddy. This rapid deceleration, and the left tire being off the pavement, caused the rear of the plane to “rise” and the propeller struck the runway. With this motion, and the left tire being below the pavement, the airplane pivoted to the left, and the left-wing tip struck the surface. The airplane came to rest on its landing gear, just off the runway surface.