We demonstrate the strong coupling of both magnons and phonons to terahertz (THz) frequency electromagnetic (EM) waves confined to a photonic crystal (PhC) cavity. Our cavity consists of a two-dimensional array of air-holes cut into a hybrid slab of ferroelectric lithium niobate (LiNbO3) and erbium orthoferrite (ErFeO3), a canted antiferromagnetic crystal. The phonons in LiNbO3 and the magnons in ErFeO3 are strongly coupled to the electric and magnetic field components of the confined EM wave, respectively. This leads to the formation of new cavity magnon-phonon-polariton modes, which we experimentally observe as a normal-mode splitting in the frequency spectrum and an avoided crossing in the temperature-frequency plot. The cavity also has a mode volume of V = 3.4 × 10 −3 λ 3 ≃ 0.5(λ/n) 3 µm 3 and can achieve a Q-factor as high as 1000. These factors facilitate the pursuit of the fields of THz cavity spintronics and quantum electrodynamics. arXiv:1707.03503v1 [physics.optics]