We theoretically study magnon-phonon hybrid excitations in a square lattice ferromagnet subjected to a magnetic field by varying the field direction. The bulk bands of hybrid excitations, which are referred to as magnon-polarons, are investigated by considering all three phonon modes: Vertical phonon, transverse phonon, and longitudinal phonon. We show that the topological properties of three hybridizations are different in terms of the Berry curvature and the Chern numbers. We also find that the topological properties of the bands can be controlled by changing the direction of the magnetic field, exhibiting one or more topological phase transitions. The dependence of thermal Hall conductivity as a function of magnetic field direction is proposed as an experimental probe of our theoretical results.