We consider anisotropic colloidal particles with dumbbell or lens shapes that are immersed in a critical binary fluid mixture. The orientation-dependent long-ranged universal interactions mediated by the critical solvent between a particle and a wall or between two particles are investigated for mesoscopic particle sizes small compared to the correlation length and interparticle distances. Exact results are obtained using a "small particle operator expansion." The amplitudes of the isotropic and anisotropic operators in the expansion depend on the size and aspect ratio of the dumbbell or lens and are determined by density profiles in the Ising model at the critical point in a wedge geometry with symmetry-breaking fixed-spin boundary conditions. Dumbbells and ellipsoids with a symmetry preserving surface are also considered. (C) 2004 American Institute of Physics.