Multi-access edge computing (MEC)-enabled integrated space-air-ground networks have drawn much attention recently, as they can provide communication and computing services to wireless devices in areas that lack terrestrial base stations (TBSs). They could make it possible for battery-powered Internet of Things (IoT) devices to offload their computation tasks to MEC-enabled unmanned aerial vehicles (UAVs) assisted aerial networks and low earth orbit (LEO) satellites and thus reduce their energy consumption and allow them to complete the execution of tasks on time. However, due to the limited computation capacity of the MEC servers at UAVs and satellites, an efficient offloading decision and computation resource allocation scheme is essential. Therefore, this paper investigates the problem of minimizing the latency experienced by the wireless devices in the MEC-enabled integrated space-air-ground network by optimizing the offloading decision while assuring the energy constraints of both devices and UAVs. The problem is proved to be a non-convex problem, and the block successive upper-bound minimization (BSUM) method is proposed as a solution. Finally, extensive simulation results are presented to exhibit the effectiveness of the BSUM algorithm in solving the proposed problem.