Effective confinement of light and sound is achieved through a one-dimensional phoxonic crystal (PxC) cavity. In particular, co-localization of gigahertz phonons and infrared photons in a cavity created by introducing a defect inside a multilayer PxC has been performed. The incident elastic waves can control the refractive index variation of the dual phononic-photonic cavity layer. We also studied the acousto-optic (AO) effect in four AO materials, each located in the cavity layer between two identical Bragg mirrors. The cavities are designed to have high-quality factors for both photon and phonon resonances, which are proportional to their lifetime and allow for a much stronger photon-phonon interaction. The AO effect causes a shift in the optical mode of the photonic band gap. The values of the refractive index of the AO cavities layer are estimated as a function of time based on the elastic strain perturbation using the relevant photo-elastic relations. The phoxonic band gaps and transmission spectra for both unperturbed and elastically perturbed PxC structures are derived depending on the transfer matrix method. In our results, the selected AO cavity of PbMoO4 provided the strongest AO coupling, in which the maximum wavelength shift of the resonant photonic modes reached 113.3 nm. In addition, 11.9 nm is the maximum displacement amplitude of the confinement elastic wave of the same nanocavity. The TeO2 cavity provided the highest Q values for both photonic and phononic modes of 7093 and 175, respectively. We think this research could open the way to study the properties of linear elastic materials to design extremely miniaturized AO devices.