To solve the problem of “first-kilometer” distribution difficulties in rural areas, we propose a transportation method using unmanned aerial vehicles (UAVs) for delivery. The mountainous environment of Fengshan County in Guizhou is first simulated as the UAV delivery environment. A differential evolution strategy based on the improved whale optimization algorithm (DEIWOA) combined with multisource heterogeneous sensors is then proposed to solve the UAV obstacle avoidance path. After the UAV’s delivery path is planned using the DEIWOA algorithm, the multisource heterogeneous sensor is used to perform obstacle avoidance among multiple UAVs and path correction of UAVs in actual situations. Afterwards, to minimize the delivery cost of UAVs, a multi-UAV cargo delivery model is built with the optimization goal of minimizing the transportation cost and time window violation cost. This UAV scheduling model is solved using the proposed DEIWOA algorithm. Finally, simulations are performed to compare the proposed method with the cutting-edge algorithms. The obtained results show that the proposed DEIWOA algorithm can provide a better plan of the UAV path and reduce the cost of logistics scheduling. It can also provide support for UAV logistics and distribution in mountainous areas in actual situations.