The Piper Pawnee was spraying chemical in the local area. The strip being used was 350 m in length, and had several trees at the far end, some 16 m to the left of the departure path. There was a crosswind from the right of about 10 to 12 knots. The strip surface was soft, but the pilot reported he had not experienced any problems during a previous takeoff, although the aircraft was unladen. Prior to the next takeoff the aircraft was loaded with chemical. The pilot subsequently reported that late in the takeoff run, with the engine operating normally, the aircraft suddenly slowed and slewed left about 20 degrees, before again accelerating normally. The aircraft lifted off at approximately 65 knots, displaced to the left and further along the strip than on the previous takeoff. The pilot reported he was unable to prevent the aircraft colliding with the trees located to the left of the normal departure path. This resulted in the aircraft rolling inverted and striking the ground. It is considered the left mainwheel may have struck a soft area of the strip during the takeoff run, causing the initial left yaw and slight deceleration.