The unmanned aerial vehicle (UAV) enabled mobile edge computing (MEC) has been deemed a promising paradigm to provide ubiquitous communication and computing services for the Internet of Things (IoT). Besides, by intelligently reflecting the received signals, the reconfigurable intelligent surface (RIS) can significantly improve the propagation environment and further enhance the service quality of the UAV-enabled MEC. Motivated by this vision, in this paper, we consider both the amount of completed task bits and the energy consumption to maximize the energy efficiency of the RIS-assisted UAV-enabled MEC systems with non-orthogonal multiple access (NOMA) protocol, where the bit allocation, transmit power, phase shift, and UAV trajectory are jointly optimized by an iterative algorithm with a double-loop structure based on the Dinkelbach's method and block coordinate decent (BCD) technique. Simulation results demonstrate that: 1) our proposed algorithm can achieve higher energy efficiency than baseline schemes while satisfying the task tolerance latency; 2) the energy efficiency first increases and then decreases with the increase of the mission period and the total amount of task-input bits of IoT devices; 3) the energy efficiencies of schemes with imperfect channel state information (CSI) are lower than corresponding schemes with perfect CSI, and the performance gain of NOMA over OMA diminishes under the imperfect CSI.