Computational offloading has become an enabling component for edge intelligence in mobile and smart devices. Existing offloading schemes mainly focus on mobile devices and servers, while ignoring the potential network congestion caused by tasks from multiple mobile devices, especially in wireless multi-hop networks. To fill this gap, we propose a low-overhead, congestion-aware distributed task offloading scheme by augmenting a distributed greedy framework with graph-based machine learning. In simulated wireless multi-hop networks with 20-110 nodes and a resource allocation scheme based on shortest path routing and contention-based link scheduling, our approach is demonstrated to be effective in reducing congestion or unstable queues under the context-agnostic baseline, while improving the execution latency over local computing.