Deploying learned multi-robot models on heterogeneous robots remains challenging due to hardware heterogeneity, communication constraints, and the lack of a unified execution stack. This paper presents NeuroMesh, a multi-domain, cross-platform, and modular decentralized neural inference framework that standardizes observation encoding, message passing, aggregation, and task decoding in a unified pipeline. NeuroMesh combines a dual-aggregation paradigm for reduction- and broadcast-based information fusion with a parallelized architecture that decouples cycle time from end-to-end latency. Our high-performance C++ implementation leverages Zenoh for inter-robot communication and supports hybrid GPU/CPU inference. We validate NeuroMesh on a heterogeneous team of aerial and ground robots across collaborative perception, decentralized control, and task assignment, demonstrating robust operation across diverse task structures and payload sizes. We plan to release NeuroMesh as an open-source framework to the community.