By introducing Mobile Edge Computing (MEC) into satellite networks enables the sinking of cloud computing power closer to users and improves user experience. However, the limited resources of edge servers cannot meet the huge demand for computing resources in remote areas, which may lead to the increase in task processing delay and reduce the communication efficiency. Therefore, efficient resource allocation strategies and task offloading decisions are needed to reduce the total delay of on Orbit Edge Computing systems. Based on the above problems, this paper proposes a joint resource allocation and task offloading strategy, which is mainly divided into two parts, the optimal resource allocation through Lagrange multiplier method, and the optimization of offloading strategy for different service types through the improved Grey Wolf Optimization. Simulation results demonstrate that the proposed algorithm can reduce the total system delay effectively.