The pilot filed a VFR flight plan, but did not activate it after takeoff. While en route, he encountered deteriorating weather and obtained an IFR clearance. As he continued, he entered an area of thunderstorms, turbulence, and heavy rain. As the pilot was about to depart the area of bad weather, the aircraft turned nearly 180 degrees and began heading toward the edge of a thunderstorm. The pilot was advised of his heading deviation and was provided a vector away from the storm and back on course. At about the same time, two witnesses on the ground heard an aircraft in the same area. They reported that the engine was revving as if the plane was diving up and down. Both reported that the plane sounded like it was leaving the area, then it returned and circled before crashing. The plane impacted in a right bank, nose low attitude. After impact, the wreckage scattered over a 200 by 400 ft area. An examination of the engine revealed no precrash failures.