We present NeuRIO, a streaming neural estimator for anchor-free 6-DoF relative inertial odometry using only identified inter-robot bearings, ranges, and IMU measurements. NeuRIO canonicalizes measurements into gravity-aligned coordinates, represents robots as nodes and mutual observations as factors, and uses attention for spatial reasoning and GRUs for temporal modeling. As a graph network, NeuRIO applies shared node-wise and factor-wise operators throughout the network, enabling it to handle different team sizes and time-varying observation graphs. NeuRIO is trained on a simulator that couples various motion patterns, device-level sensor characteristics, and diverse, realistic modeled, and temporally persistent sensor corruptions. In this way, NeuRIO achieves zero-shot sim-to-real transfer. Across $24$ real-world sequences, NeuRIO achieves $14.1\,\mathrm{cm}$ position RMSE and $3.9^\circ$ rotation RMSE. More importantly, NeuRIO demonstrates strong computational scalability, maintaining an update cost below $20\,\mathrm{ms}$ with up to $400$ robots in simulation, while optimization-based methods exceed $20\,\mathrm{ms}$ at only $24$ robots. Moreover, even trained on limited team sizes, NeuRIO transfers directly to unseen larger teams without architectural or parameter changes.

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