The flight instructor reported that prior to the flight, he had measured the fuel levels in each fuel tank with a dip stick, which he had thought measured useable fuel only. He noted that the airplane had a total of 7 gallons of fuel, which he estimated was adequate for about 1.5 hours of flight time. After takeoff, they briefly flew around the area before returning to the departure airport, where they performed 4 low approaches to the runway before they performed a touch and go landing on the 5th approach. During the initial climb, about 1 hour into the flight, the engine momentarily lost power about 300 ft agl. The flight instructor took control of the airplane and turned towards the airport, however, the engine lost power again and he initiated a forced landing to a road. Shortly after, the engine regained full power for several seconds, and they were able to climb to about 75 ft agl before the engine lost power again. Subsequently, the airplane struck trees and a fence before it came to rest upright, which resulted in substantial damage to the left and right wings. The flight instructor reported that there were no preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation. He added that he misunderstood what the fuel dip stick measured, and that it measured all the fuel in the fuel tank, which included unusable fuel (1.75 gallons in each fuel tank).