The equilibrium behavior of ellipsoidal Janus nanoparticles adsorbed at spherical oil/water interfaces was investigated using dissipative particle dynamics simulations. Several phenomena were documented that were not observed on similar simulations for planar oil/water interfaces. The nanoparticles were found to yield isotropic, radial nematic phases, and axial nematic domains, depending on the nanoparticle characteristics (aspect ratio and surface chemistry), particle density at the interface, and droplet properties (curvature of the interface, and surprisingly, liquid type). When adsorbed on water droplets, the nanoparticles with high aspect ratio and few nonpolar beads on their surface can show two preferred orientation angles. Only one equilibrium orientation was found for such nanoparticles adsorbed on oil droplets. These observations might help explain a discrepancy previously reported between experimental and simulation results concerning the preferential orientation of particles at liquid-liquid interfaces. Different driving forces are responsible for the phenomena just summarized, including nanoparticle-nanoparticle and nanoparticle-solvent interactions, nanoparticle density at the interface, and droplet curvature via the Laplace pressure. The simulation results we present could be useful for engineering Pickering emulsions toward practical applications, and perhaps also for guiding new technologies for material synthesis.