Immune cells, such as macrophages and dendritic cells, can utilize podosomes, mechanosensitive actin-rich protrusions, to generate forces, migrate, and patrol for foreign antigens. Individual podosomes probe their microenvironment through periodic protrusion and retraction cycles (height oscillations), while oscillations of multiple podosomes in a cluster are coordinated in a wave-like fashion. However, the mechanisms governing both the individual oscillations and the collective wave-like dynamics remain unclear. Here, by integrating actin polymerization, myosin contractility, actin diffusion, and mechanosensitive signaling, we develop a chemo-mechanical model for podosome dynamics in clusters. Our model reveals that podosomes show oscillatory growth when actin polymerization-driven protrusion and signaling-associated myosin contraction occur at similar rates, while the diffusion of actin monomers drives wave-like coordination of podosome oscillations. Our theoretical predictions are validated by different pharmacological treatments and the impact of microenvironment stiffness on chemo-mechanical waves. Our proposed framework can shed light on the role of podosomes in immune cell mechanosensing within the context of wound healing and cancer immunotherapy.