In emergency situations, such as earthquakes, landslides and other natural disasters, the terrestrial communications infrastructure is severely disrupted and unable to provide services to terrestrial IoT devices. However, tasks in emergency scenarios often require high levels of computing power and energy supply that cannot be processed quickly enough by devices locally and require computational offloading. In addition, offloading tasks to server-equipped edge base stations may not always be feasible due to the lack of infrastructure or distance. Since Low Orbit Satellites (LEO) have abundant computing resources, and Unmanned Aerial Vehicles (UAVs) have flexible deployment, offloading tasks to LEO satellite edge servers via UAVs becomes straightforward, which provides computing services to ground-based devices. Therefore, this paper investigates the computational tasks and resource allocation in a UAV-assisted multi-layer LEO satellite network, taking into account satellite computing resources and device task volumes. In order to minimise the weighted sum of energy consumption and delay in the system, the problem is formulated as a constrained optimisation problem, which is then transformed into a Markov Decision Problem (MDP). We propose a UAV-assisted airspace integration network architecture, and a Deep Deterministic Policy Gradient and Long short-term memory (DDPG-LSTM)-based task offloading and resource allocation algorithm to solve the problem. Simulation results demonstrate that the solution outperforms the baseline approach and that our framework and algorithm have the potential to provide reliable communication services in emergency situations.