Near-inertial motions play the central role in oceanic energy cascades. Differential dynamical effects of mesoscale eddies on near-inertial oscillations (NIOs) and near-inertial internal waves (NIWs) remain poorly quantified. Using the Regional Ocean Modeling System (ROMS), idealized numerical experiments of cyclone passage display clearly different features of NIOs and NIWs under influence of meso-scale eddies. Mesoscale eddies suppress wind power input into the ocean mixed layer, reducing NIO amplitudes and accelerating post-typhoon energy decay. Anticyclonic eddies significantly enhance vertical energy transfer by strengthening inertial pumping at the mixed layer base, increasing the downward near-inertial energy flux from approximately 12% to 39% of the wind energy input, and extending energy penetration from 200 m to 2000 m depth. Their negative vorticity background reduces the effective inertial frequency, facilitating deeper wave propagation. In contrast, cyclonic eddies show limited enhancement of generation and vertical energy transfer of NIWs, confining most energy to the upper 500 m while promoting horizontal energy dispersion toward eddy peripheries. Nonlinear energy transfer analysis reveals predominantly forward transfer for mesoscale eddies, intensifying with eddy strength. These findings demonstrate that anticyclonic and cyclonic eddies play fundamentally different roles in near-inertial dynamics, with important implications for understanding oceanic internal mixing and energy pathway.