A methodology for the computation of the homogenized response of stratified piezoelectric materials is proposed. The stratified composite consists of the periodic repetition of piezoelectric layers. Its effective piezoelectric properties are obtained through a homogenization approach based on the method of oscillating functions. The method can fully consider not only the elastic attributes, but also the polarizations of the materials contained within the structure's layers. As such, it proves able to obtain the homogenized electromechanical response of the stratified piezoelectric structure in the form of parametric, closed-form expressions, which depend on the material attributes of the layers building up the repetitive unit-cell. The applicability of the method is demonstrated for the quasi-electrostatic wave propagation analysis of stratified composites using the nonlocal piezoelectric (NLPE) theory. A two-layer stratified composite is employed, created as an assembly of LiNbO3 and PVDF layers. The structure's homogenized properties are used to compute the wave propagation characteristics with and without the influence of internal length parameters of the NLPE theory. The obtained results suggest that the effective properties of the stratified composite can be handily used to compute the effect of the electric field on the longitudinal and shear modes for the propagation direction of interest.