According to a written statement from maintenance personnel, a pilot discovered the airplane's nose wheel at an "unusual angle" during a preflight inspection. The pilot reported the damage to the fixed based operator (FBO) who asked maintenance to examine the airplane. Examination of the airplane revealed damage to the nose wheel and underside of the fuselage aft of the main landing gear, and substantial damage to the rudder. The FBO contacted the certificated flight instructors and pilots of the three flights that occurred preceding the damage report. The first and third flights were airplane checkout flights with the flight instructor; the second flight was a personal flight conducted by a senior flight instructor. Written statements provided to the FBO from the two flight instructors of those flights failed to reveal who was responsible for the damage, when or where it occurred, or how it was caused. Also unknown, is why the flight instructors did not observe the damage prior to their respective flights.