We demonstrate a direct connection between the magnetic easy axis in Mn-doped GaP and epitaxial strain by a combined ferromagnetic resonance, x-ray diffraction and superconducting quantum interference device magnetometry study. The magnetic easy axis of Ga1-xMnxP is gradually rotated from the in-plane [01¯1] direction toward the film normal [100] through alloying with isovalent N which changes the strain state of the film from compressive to tensile. For a nearly lattice-matched film the strain-related component to the out-of-plane uniaxial anisotropy field is close to zero. Both in-plane and out-of-plane magnetization reversal processes are explored by a simple model that considers the combination of coherent spin rotation and noncoherent spin switching. We use our results to estimate domain-wall sizes and energetics, which have yet to be directly measured in this materials system. The band structure and electrical properties of Ga1-xMnxP imply that holes localized within a Mn-derived impurity band are capable of mediating the same anisotropic exchange interactions as the itinerant carriers in the canonical Ga1-xMnxAs system.