This paper presents a recently developed variant of phase-resolved Optical Coherence Elastography (OCE) enabling non-contact visualization of transient local strains of various origins in biological tissues and other materials. In this work, we demonstrate the possibilities of this new technique for studying dynamics of osmotically-induced strains in cartilaginous tissue impregnated with optical clearing agents (OCA). For poroelastic water-containing biological tissues, application of non-isotonic OCAs, various contrast additives, as well as drug solutions administration, may excite transient spatially-inhomogeneous strain fields of high magnitude in the tissue bulk, initiating mechanical and structural alterations. The range of the strain reliably observed by OCE varied from ±10−3 to ±0.4 for diluted and pure glycerol, correspondingly. The OCE-technique used made it possible to reveal previously inaccessible details of the complex spatio-temporal evolution of alternating-sign osmotic strains at the initial stages of agent diffusion. Qualitatively different effects produced by particular hydrophilic OCAs, such as glycerol and iohexol, are discussed, as well as concentration-dependent differences. Overall, the work demonstrates the unique abilities of the new OCE-modality in providing a deeper insight in real-time kinetics of osmotically-induced strains relevant to a broad range of biomedical applications.