The tail-wheel equipped experimental amateur-built airplane was departing from a turf runway at night. The pilot reported that he observed two deer crossing the runway and swerved to avoid them. At that time, a flashlight fell from the top of the instrument panel to the floor of the cockpit. The pilot looked down to retrieve the flashlight and did not realize that the airplane had veered off the runway. He subsequently noticed that the airplane did not feel right, looked up, and observed an approaching tree line. The pilot reduced the engine power to idle and applied brakes; however, the airplane struck trees, which resulted in substantial damage to the left wing. The pilot stated that he did not experience any mechanical malfunctions with the airplane.