We study mutual alignment and interactions between colloidal particles of dissimilar shapes and dimensions when dispersed in a nematic host fluid. Convex pentagonal and concave starfruit-shaped nanoprisms and microspheres induce dipolar or quadrupolar director structures. The ensuing elastic pair interactions between microspheres and nanoprisms are highly dependent on the nanoparticle shape being omnidirectionally attractive for convex prisms but strongly anisotropic for concave prisms. Elastic deformations due to spherical particles cause well-defined alignment of complex-shaped nanoparticles at distances much larger than the microsphere size. We characterize distance and angular dependencies of elastic pair interaction forces, torques, and binding energies. The studied elasticity-mediated self-assembly of metal and dielectric nanoparticles with dissimilar shapes and sizes opens new possibilities for self-assembly based fabrication of structured mesoscopic composites with predesigned properties.