This paper investigates a reconfigurable intelligent surface (RIS)-aided unmanned aerial vehicles (UAVs) system with non-orthogonal-multiple access (NOMA), where the transmit signals from multiple UAVs to ground users are strengthened through a RIS. An innovative framework is designed to minimize the total power consumption of the system, by jointly optimizing the position of UAVs, RIS reflection coefficients, active beamforming vectors and decoding order. To solve this problem, we first consider the sub-solution of the UAV's location which can be achieved via the successive convex approximation (SCA) and maximum ratio transmission (MRT). By applying the Gaussian randomization procedure, we then yield the closed-form solution for RIS phase coefficients. Subsequently, the transmit power is obtained by the standard convex optimization methods. Finally, a dynamic-order decoding scheme is proposed to optimize the decoding order. Simulation results show that the resource allocation scheme can obviously reduce the total power consumption compared to the benchmark schemes.