In this paper, we address the resource allocation problem for task offloading from Internet of Things (IoT) devices to a non-terrestrial network. The proposed architecture contains clusters of IoT devices that can either execute their computational tasks locally or offload them to a dedicated unmanned aerial vehicle (UAV) functioning as a multi-access edge computing (MEC) server. The UAV can process the tasks itself or further offload them to an available high-altitude platform station (HAPS) or to a low-earth orbit (LEO) satellite within lineof-sight for remote computation. We formulate an optimization problem that aims to minimize the weighted sum of the total task-execution delay and the energy consumption of the IoT devices. Due to non-convexity of the problem and the inherent complexity-performance trade-off in optimization algorithms, we propose a set of low-complexity solutions. These include optimal methods based on convex subproblem decomposition and a greedy heuristic guided by convex optimization criteria. The framework jointly optimizes the computing resources and transmission power of IoT devices, the digital precoders and combiners at the UAV, the computing resources at the remote nodes (UAV, HAPS, and LEO), as well as task offloading decisions and subchannel allocation through a one-shot block coordinate descent approach. Simulation results highlight the performance gains of the proposed methods, demonstrating the impact of algorithmic complexity on key system metrics and the benefits of incorporating multiple non-terrestrial nodes compared to architectures lacking such capabilities.