A magnon junction consisting of ferromagnetic/antiferromagnetic/ferromagnetic insulators can manipulate the transmission of magnon current through adjusting magnetic moment alignment, offering potential for ultra-low power magnon circuits. This study employs density functional theory calculations and atomic simulations to investigate the strain-dependent modulation of magnon current transport in CoFe2O4/NiO/CoFe2O4 junctions induced by bulk acoustic waves. Our results demonstrate that strain significantly alters the magnetic anisotropy energy of both NiO and CoFe2O4, with NiO favoring in-plane magnetic anisotropy under various strains and CoFe2O4 exhibiting a transition from in-plane to perpendicular magnetic anisotropy. Additionally, controlling the magnetic anisotropy energy of NiO and CoFe2O4 allows for the regulation of magnon current transmission, providing a novel approach to optimize magnonic device performance. These findings highlight the potential of strain as a tunable parameter in the design of advanced magnonic devices.