<p>The rapid development of Space-Air-Ground Integrated Network (SAGIN) has given rise to collaborative computing architectures, where satellites, Unmanned Aerial Vehicles (UAVs), and ground terminals cooperate to support ubiquitous coverage and real-time services. However, the heterogeneity of multi-modal tasks poses significant challenges to traditional offloading strategies. Traditional static priority methods cannot solve the dynamic coupling between time-varying network states and task characteristics, resulting in QoS violations and suboptimal resource allocation. To solve these problems, we propose a hierarchical offloading and collaborative computing framework driven by dynamic priority of mobile users’ tasks. First, we establish a multi-dimensional task priority evaluation model and combine the satellite coverage time prediction and the UAV trajectory error to modify the task priority in real time. Second, we design a hierarchical game mechanism based on cloud-edge-device collaboration, where UAVs/satellites and mobile devices make distributed bidding decisions and priority-aware offloading decisions. Then, we propose a Dynamic Priority-driven Hierarchical Game Multi-Agent Proximal Policy Optimization (DP-HG-MAPPO) algorithm to integrate task offloading and resource pricing strategies to achieve optimal trade-offs among delay, energy efficiency, and load balancing. Using multi-dimensional feature modeling, game-reinforcement learning fusion and adaptive threshold mechanism, we achieve efficient matching between multi-type tasks and multi-level resources. The simulation results show that, compared with the existing benchmark algorithms, our proposed method improves the task completion rate, delay satisfaction degree of high priority tasks and energy efficiency by 11.7%, 18.3% and 28.8% respectively in the dynamic and resource-constrained SAGIN environment.</p>