Deformation and stress in battery electrode materials are strongly coupled with diffusion processes, and this coupling plays a crucial role in the chemical and structural stability of these materials. In this work, we performed a comparative study of the mechanical characteristics of two model materials (lithiated and sodiated germanium (Ge)) by nanoindentation. A particular focus of the study was on the indentation size effects and harnessing them to understand the chemo-mechanical interplay in these materials. While the quasi-static measurement results showed no significant size dependence, size effects inherent in the nanoindentation creep response were observed and utilized to investigate the deformation mechanism of each material. Supplemented by computational chemo-mechanical modeling, we found that lithiated Ge creeps through a stress-gradient-induced diffusion (SGID) mechanism but a model combining the SGID and conventional shear transformation deformation (STD) mechanisms was needed to capture the creep behavior of sodiated Ge. Broadly, this work reveals the importance of stress-diffusion coupling in governing the deformation of active electrode materials and provides a quantitative framework for characterizing and understanding such coupling.