In this paper, a cooperative non-orthogonal multiple access (NOMA) mobile edge computing (MEC) network aided by reconfigurable intelligent surfaces (RIS) and simultaneous wireless information and power transfer (SWIPT) is considered, where the transmitters offload parts of their computing tasks to the MEC server via a relay and an RIS for enhancing the transmission environment. The goal is to minimize the task delay and energy consumption for the considered networks by jointly designing the RIS's reflection beamforming vector, the power splitting (PS) ratio, the power allocation factors of the relay, as well as the offloading transmit power and the offloading task ratio. To solve the proposed problems, an iterative optimization algorithm based on the successive convex approximation (SCA) method and the penalty method is proposed to decompose the formulated problems into two sub-problems. In particular, we jointly optimize the PS ratio, the power allocation coefficients and the edge computing resource based on the SCA technology, and then the penalty method is used to optimize the RIS's reflecting beamforming vector. Simulation results illustrate that the proposed NOMA-MEC networks aided by RIS and SWIPT are superior to the conventional orthogonal multiple access MEC networks with SWIPT aided by RIS in terms of task delay and energy consumption.