Motivated by the recent progress of phonon-mediated control in quantum spin devices, we propose a possibility of hybrid measurement using electron paramagnetic resonance (EPR) and a surface acoustic wave (SAW). Considering quadrupole-strain (QS) couplings suggested for silicon vacancies, we present a minimum model of the two-level system to investigate a magnetoacoustic resonance (MAR) coupled to various strain modes driven by the SAW. The longitudinal and transverse QS couplings can be changed by rotating a magnetic field, which depends on a combination of the strain modes. Using the Floquet theory, we elucidate each coupling effect on the time-averaged transition probability, especially focus on a single-phonon transition process. The important result is that the longitudinal QS... coupling brings about a sharp photon-assisted resonance and leads to an abrupt change in the field-angle dependent transition probability. Since this phonon transition process is always accompanied by the photon transition, the field angle for the sharp resonance peak can be detected by the EPR measurement. The hybrid EPR-MAR measurement is useful to confirm the existence of quadrupole degrees of freedom strongly coupled to elastic strains, and thus it is expected to be a complementary probe for the precise evaluation of quadrupole properties.