The pilot reported that, while on a 3-mile base leg, he encountered a flock of large birds. He aborted the base leg and rapidly descended the airplane to avoid the birds, but the birds followed. The pilot continued the dive and saw power lines nearby. He made an "evasive maneuver (dive down)" to avoid the power lines, but the vertical stabilizer struck the power lines, shearing off the vertical stabilizer and rudder. The pilot maintained airplane control, climbed the airplane, declared "mayday," and requested flight following to an airport without a crosswind for landing. He approached at a higher airspeed to reduce the airplane's left turning tendencies, and during the landing roll, the airplane veered left off the runway into an adjacent field. The airplane sustained substantial damage to the vertical stabilizer and rudder. The pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.