The pilot stated that he and his friend, who is also a flight instructor, were performing touch-and-go landings at different airports. After his last touch-and-go, and during climb out, he saw some turkey buzzards flying above the airplane. He decided to turn to the right to avoid the birds but one of the buzzards hit the propeller and the airplane started to violently shake. The flight instructor, seated in the rear seat, shut off the engine and took over control of the airplane. The flight instructor then located a field to land in. They landed with a tailwind and during the landing roll, they were getting close to some trees at the end of the field. The pilot was not sure if he depressed the brakes or the flight instructor did, or they both did, but the airplane nosed over and came to rest inverted about 40 feet away from the trees, resulting in substantial damage to the rudder and wings.