We propose a scheme to achieve bipartite and tripartite entanglement in a hybrid cavity optomagnonic system, which consists of a microwave cavity with two yttrium iron garnet spheres (YIG1 and YIG2), and YIG1 also serves as a whispering-gallery-mode (WGM) resonator. Based on the moderately strong-coupling triple-resonant interaction of the optomagnonic system, magnon-magnon and optical-microwave entanglement can be achieved. In addition, this scheme enables controlled transfer of entanglement among different subsystems. The entangled partner of the magnon mode in YIG1 can be easily switched among the optical, magnon, and microwave mode by adjusting the optical detuning, thereby achieving entanglement transfer. Tripartite optical-magnon-magnon, optical-magnon-microwave, and magnon-magnon-microwave entanglement can also be obtained and can be transferred conveniently by adjusting the detuning and the driving power. These results provide a flexible controllability of bipartite and tripartite entanglement and their transfer for quantum nodes integrating multiple physical systems (optical, magnonic, and microwave), which can be applied in entanglement-based quantum applications.