In this paper, we explore optimization-based and data-driven solutions in a reconfigurable intelligent surface (RIS)-aided multi-user mobile edge computing (MEC) system, where the user equipment (UEs) can partially offload their computation tasks to the access point (AP). We aim at maximizing the total completed task-input bits (TCTB) of all UEs with limited energy budgets during a given time slot, through jointly optimizing the RIS reflecting coefficients, the AP's receive beamforming vectors, and the UEs' energy partition strategies for local computing and offloading. A three-step block coordinate descending (BCD) algorithm is first proposed to effectively solve the non-convex TCTB maximization problem with guaranteed convergence. In order to reduce the computational complexity and facilitate lightweight online implementation of the optimization algorithm, we further construct two deep learning architectures. The first one takes channel state information (CSI) as input, while the second one exploits the UEs' locations only for online inference. The two data-driven approaches are trained using data samples generated by the BCD algorithm via supervised learning. Our simulation results reveal a close match between the performance of the optimization-based BCD algorithm and the low-complexity learning-based architectures, all with superior performance to existing schemes in both cases with perfect and imperfect input features. Importantly, the location-only deep learning method is shown to offer a particularly practical and robust solution alleviating the need for CSI estimation and feedback when line-of-sight (LoS) direct links exist between UEs and the AP.