This paper studies a mobile edge computing system where two solar-powered nodes (i.e., a relay and an intelligent reflecting surface (IRS)) assist a user node in task offloading to an access point. To save the long-term energy consumption at the user, a novel protocol is first proposed so that the system can adaptively select the operating modes. Then, based on this protocol, the optimization problem of the system is formulated to minimize the energy consumption of task offloading and computing at the user by optimizing the system operation modes and the resource allocation in each mode, subject to the battery energy states of the IRS and the relay with the energy causality constraints. The problem is solved using the Lyapunov optimization framework and an alternating optimization algorithm. Simulation results show that the proposed system optimization scheme can save 70%-95% of energy consumption as compared to the baseline schemes.