The flight instructor reported that the student pilot was flying S-turns over a road at 1,000 feet above ground level when a bald eagle struck the right horizontal stabilizer. The flight instructor took the controls, declared an emergency, and proceeded to land at the nearest airport. The control yoke was “buffeting,” but the engine continued to run smoothly. On final approach, the flight instructor noticed that the rudder controls were impaired; however, the wind was calm so the landing was without incident. The examination of the airplane revealed that there was a large indentation on the right horizontal stabilizer with bird feathers embedded in it. The right side of the horizontal stabilizer was canted. In addition, the tail cone had been pushed upward and was in contact with the rudder, impeding its movement.