The pilot reported that while en route he noted that the fuel gauges were fluctuating and eventually indicated empty. He declared an emergency and diverted to a nearby airport. During the approach the airplane was too high and despite a slip and s-turns he landed long, overran the departure end of the runway, and struck a fence. The airplane sustained substantial damage to the fuselage. The pilot reported that other than the erratic fuel indication on the fuel gauges, no other mechanical malfunctions or failures existed with the airplane prior to the accident that would have precluded normal operation. He added that at the time of landing, the engine was still running and a postaccident examination of the airplane revealed an adequate amount of fuel in the fuel tanks.