The pilot was conducting a visual flight rules (VFR) cross-country flight at 5,500 ft mean sea level (MSL) above a cloud layer, and the airplane was not equipped with an attitude indicator or flight instruments to operate in instrument meteorological conditions. According to the pilot, the weather was forecast VFR at her destination. While en route, a cloud layer above her started lowering, so she descended to 5,000 ft MSL. The pilot could see blue sky between the layers when the two layers started to come together and then she inadvertently entered instrument meteorological conditions (IMC). The pilot transitioned to an "inside instrument scan", turned on carburetor heat, and added full power to attempt to climb to find VFR conditions. After climbing 300 to 500 ft and about 5 minutes after entering the clouds, the pilot noticed a right turn had developed as confirmed on the heading indicator and her electronic flight device. The right turn became tighter, and the pilot recognized she was disoriented, and the airplane was descending. She elected to perform corrective action for a nose low unusual attitude and attempted to descend to visual flight conditions. The airplane broke out of the clouds about 1,500 ft above the ground (AGL) in a 25° to 30° right bank and 10° to 15° nose low attitude. The pilot recovered to level flight and added full power. The airplane would not accelerate above 60 to 65 knots in level flight and the pilot felt the rudder was ineffective. The pilot elected to conduct a precautionary landing to nearby field that was muddy due to recent rains. During the landing, the airplane flipped over when the wheels dug into the ground. The vertical stabilizer, rudder, and both wings sustained substantial damage. Examination of the airplane revealed flight control continuity to all flight control surfaces. The pilot reported that the airplane was operating normally prior to entering IMC conditions..