In field battlefield environments lacking infrastructure, there are many different heterogeneous intelligent devices with different resource configurations and mobility. If resource-poor devices offload tasks to nearby resource-rich devices for processing, the resource advantages of groups in the battlefield environment can be fully utilized to satisfy the arithmetic requirements of various tasks as much as possible. In this paper, we introduce pervasive edge computing (PEC) to realize task offloading and resource sharing in the scenario. A dynamic prioritized task offloading strategy with delay constraints (PWRR-BP) is proposed to address the fact that some of the tasks generated by the device have the constraint limitation of completing them within the deadline time, which needs to minimize the queuing and waiting delay as much as possible. This strategy dynamically assigns priorities and weights to different task types, while considering the impact of mobility on the scheduling strategy. Subsequently, in order to enable the device to accurately perceive the surrounding load situation, the expected waiting delay of the task on the device is predicted using a BP neural network to provide a more accurate basis for the offloading decision. The experimental results show that the PWRR-BP strategy optimizes the queue scheduling efficiency, which can effectively reduce the queue waiting delay of the delay-sensitive tasks in the scenario, and at the same time improve the overall task completion rate of the scenario.