Internet of Things (IoT) computing offloading is a challenging issue, especially in remote areas where common edge/cloud infrastructure is unavailable. In this paper, we present a space-air-ground integrated network (SAGIN) edge/cloud computing architecture for offloading the computation-intensive applications considering remote energy and computation constraints, where flying unmanned aerial vehicles (UAVs) provide near-user edge computing and satellites provide access to the cloud computing. First, for UAV edge servers, we propose a joint resource allocation and task scheduling approach to efficiently allocate the computing resources to virtual machines (VMs) and schedule the offloaded tasks. Second, we investigate the computing offloading problem in SAGIN and propose a learning-based approach to learn the optimal offloading policy from the dynamic SAGIN environments. Specifically, we formulate the offloading decision making as a Markov decision process where the system state considers the network dynamics. To cope with the system dynamics and complexity, we propose a deep reinforcement learning-based computing offloading approach to learn the optimal offloading policy on-the-fly, where we adopt the policy gradient method to handle the large action space and actor-critic method to accelerate the learning process. Simulation results show that the proposed edge VM allocation and task scheduling approach can achieve near-optimal performance with very low complexity and the proposed learning-based computing offloading algorithm not only converges fast but also achieves a lower total cost compared with other offloading approaches.