Olfaction provides critical information about airborne chemical cues, yet it remains largely underexplored in embodied AI, with limited prior machine olfaction work focusing primarily on semantic odor perception. We introduce OdorSpaces, a physics-based simulation platform and benchmark for visual-olfactory embodied navigation. OdorSpaces augments Habitat-Sim with 3D odor transport and dispersion simulated by Fire Dynamics Simulator (FDS), enabling agents to navigate photorealistic indoor environments using both visual and olfactory observations. The benchmark includes two representative source-seeking scenarios: invisible gas-leak localization and early-stage fire localization. We develop an initial multimodal reinforcement learning policy that integrates visual observations and olfactory measurements over time. Experiments show that the policy outperforms a diverse set of baselines, establishing a strong reference for future research on visual-olfactory embodied navigation.