In this paper, energy efficiency is analyzed in a reconfigurable intelligent surface (RIS) aided mobile edge computing (MEC) network. The offloading decisions at the user equipments (UEs), computational resource allocation strategies at the MEC server, and the choice of RIS reflecting coefficients are jointly taken into consideration. To address the latency requirements, the use of finite blocklength (FBL) codes is considered in the uplink transmission, which also utilizes non-orthogonal multiple access (NOMA) for improved efficiency in resource usage. A UE-grouping scheme is introduced to group the UEs for NOMA transmission, and a dynamic CPU frequency allocation algorithm at the MEC server is developed. The primary objective is to maximize the overall energy efficiency of the RIS-aided MEC network under both decoding error rate and latency constraints. For this purpose, a four-step algorithm is devised to optimize RIS reflecting coefficients, offloaded data bits, offloading blocklength, and MEC frequency allocations. Simulation results illustrate the effectiveness of our proposed algorithm and the importance of UE scheduling with NOMA transmission.