The convergence of 5G networks and IoT technologies is accelerating the power system into smart grid, and terminals are unable to meet service quality requirements with their own resources. Edge computing has emerged as a new solution. Considering the computing resources of idle devices, the offloading strategy and resource allocation method are jointly optimized to minimize the average delay of task procedure in a communication system with multiple terminals and single edge computing server. The problem can be divided into two subproblems, resource allocation optimization subproblem and task offloading strategy subproblem, which can be solved by Lagrange multiplier method and Nash equilibrium game algorithm, respectively. An enhanced particle swarm optimization algorithm is also introduced to generate the initial offloading strategy. Simulation results indicate that the proposed algorithm can significantly reduce the average delay of task procedure.