The pilot reported that he was flying at a low altitude over a river into hazy conditions and looking directly into the setting sun. The pilot stated that as he was preparing to divert to miss a flock of birds the airplane impacted a set of transmission wires, which struck and severed the airframe's wing support structures. The impact with the wires forced the airplane to a lower altitude and under a bridge in the airplane's flight path. After flying under the bridge and exiting on the opposite side, the airplane impacted a second set of transmission wires with the airplane's landing gear legs. The pilot stated that he then elected to make a forced landing on a river gravel bar; the airplane landed without incident and came to rest upright. A witness, who was camping nearby, observed the airplane flying about 20 to 40 feet above the river before going out of sight. The witness reported, "Approximately 5 seconds later I heard a 'large impact,' followed by an electrical discharge sound and the power going out at the campground."