<p>In this present, the finite element approach is employed to analyze the free oscillation, static and dynamic buckling of skew-nanoplate made of piezoelectric materials with variable thickness resting on variable Pasternak medium in a hygro-temperature environment. This study is a wonderful combination of Kirchhoff plate theory, nonlocal strain gradient hypothesis, and surface effect and Hamilton’s principle to derive the general equilibrium equation of the plate. A four-node quadrilateral plate element with six degrees of freedom per node is developed using a Hermit C²-level non-conforming shape function. This element offers high accuracy and fast convergence for a variety of shapes and boundary conditions, outperforming lower-order elements. Bolotin’s method is applied to determine the dynamic instability region of the non-uniform piezoelectric skew nanoplate. The accuracy of the present approach is validated through numerical comparisons with established data. Furthermore, the effects of parameters such as residual surface stress, applied voltage, temperature gradient, moisture, elastic foundation stiffness, thickness variation, skew angle, geometric factors, and boundary conditions on free oscillation and stability of skew nanoplate are thoroughly assessed. The present study will offer the physical insights required to model size-dependent multifunctional systems for active control of mechanical characteristics and electromechanical energy harvesting, given the recent developments in nanoscale manufacturing.</p>