In this paper, we propose a scheme for measurement-based control of hybrid Einstein-Podolsky-Rosen (EPR) entanglement and steering between distant macroscopic mechanical oscillator and yttrium iron garnet (YIG) sphere in a system of an electromechanical cavity unidirectionally coupled to an electromagnonical cavity. We reveal that when the output of the electromagnonical cavity is continuously monitored by homodyne detection, not only the phonon-magnon entanglement and steering but also the purities of the phononic, magnonic and phonon-magnon states are considerably enhanced. We also find that...