The pilot was flying at 840 feet over a bayou canal when a large bird contacted the leading edge of the right wing. The pilot stated he thought the bird was possibly either an eagle or a vulture. He stated he immediately felt a vibration in the control yoke, and had to apply left aileron and left rudder to keep the airplane from rolling to the right. The pilot assessed the aircraft's control capability and decided to return to the St. Charles Airport (LS40). The pilot contacted the air traffic control (ATC) at the nearby New Orleans International Airport (MSY) and requested that there be emergency vehicles standing by at LS40 when he landed. As he approached the airport, the pilot extended 10 degrees of flaps and slowed the airspeed to 120 mph, still applying left aileron and rudder. The pilot turned the airplane to final approach and the continued to decrease the airspeed to land. As the airspeed reached 90 to 100 mph, the right wing dropped and the airplane rolled between 45 and 90 degrees to the right. The pilot added full power, retracted the flaps, and applied full left aileron and left rudder. The airplane descended to an altitude of 100 feet before the pilot was able to level the wings and begin a climb. The pilot realized he needed to keep the airspeed above 120 mph to maintain control of the airplane so he contacted the ATC tower at MSY and requested to land there so that he would have a longer runway and could land at a higher than normal airspeed. The pilot landed the airplane at MSY without further incident. A postaccident examination of the airplane revealed the airplane sustained substantial damage to the leading edge of the right wing.