The magnetoelectric behavior of epitaxial Fe-Ga microstructures on top of a (001)-oriented PMN-PT piezoelectric substrate is imaged with magnetic X-ray microscopy. Additionally, the micron-scale strain distribution in PMN-PT is characterized by X-ray microdiffraction and examined with respect to the results of the Fe-Ga magnetoelectric switching. The magnetic reorientation of Fe-Ga is found to be strongly correlated with size, shape, and crystallographic orientation of the microstructures. In the case of square-shaped structures, size dictates the influence of the strain distribution on both the initialization of the ground state and on the magnetic reorientation during application of voltage. On the other hand, elliptical microstructures demonstrate completely different magnetic responses depending on the relative orientation of their long axis with respect to the crystallographic directions of the PMN-PT. This study demonstrates that engineering the behavior of highly magnetostrictive epitaxial microdevices is possible. It further elucidates that voltage-induced actuation can be largely tuned to achieve the desired type of magnetic switching ranging from vortex circulation reversal, domain wall motion, to a large rotation of magnetization. Because of the outstanding properties of the investigated material system, the reported findings are expected to be of great interest for the realization of next-generation energy-efficient magnetic memory and logic devices.