In this work, molecular dynamics simulations are conducted to investigate the shock responses and corresponding deformation mechanisms in single crystalline (SC) and nanocrystalline (NC) microstructure of the medium entropy alloy (MEA) CoCrNi. The effects of lattice distortion (LD) and chemical short-range order (CSRO) on the shock wave propagation, defect evolution, and the cavitation process are explored to distinguish the unique shock properties of MEA. The results reveal an anomalous anisotropy in the Hugoniot elastic limit different from that seen in pure FCC metals since LD reduces the barrier for Shockley partial (SP) formation but increases the resistance for SP propagation. With sufficient dislocations nucleated in the first shock compression stage, LD aids in the formation of nanotwins by slowing down dislocation propagation in the following release and tension stages. However, because a higher degree of CSRO increases the average intrinsic stacking fault energy above that of the random material, more stacking faults annihilate in the release stage, reducing the chances for nanotwinning. We show that voids prefer to nucleate at Ni segregation sites (with high CSRO) due to the large hydrostatic tensile strain created by the lattice mismatch between the neighboring Ni and CoCr regions, and moreover, the nucleation event favors the grain boundary during spallation in NCs.