An optical resonance method for the determination of the strain- and stress-optical coefficients of optically transparent polymers is presented and exemplified for monodisperse and bidisperse molecular weight polystyrene (PS). This method employs whispering gallery modes (WGMs) resonation inside a spheroid polymeric cavity, suspended on an optical fiber taper waist, which, in turn, is used for subjecting the polymeric resonator to controlled strain conditions. The wavelength shifts of equal order transverse electric and transverse magnetic polarization WGMs are measured, as well as their relative birefringence versus applied strain. For monodisperse PS microspheroids (2 and 50 kDa) the stress-optical coefficient is negative, contrary to the results for bulk PS in the glassy state indicating different phenyl group orientation of the PS monomer with respect to the strain direction. In the bidisperse (2 and 50 kDa) spheroid with a symmetric monomer composition, local structural irregularities are probably responsible for the observed coupling between WGMs. The method possesses metrological capabilities for probing the molecular orientation of polymer-based resonators.