The surface free energy of ideal hard rods near curved hard surfaces is determined to second order in curvature for surfaces of general shapes. In accordance with previous results for spherical and cylindrical surfaces it is found that this quantity is nonanalytical when one of the principal curvatures changes signs. This prohibits writing it in the common Helfrich form. It is shown that the nonanalytical terms are the same for any aspect ratio of the rods. These results are used to find the equilibrium shape of vesicles immersed in solutions of rodlike (colloidal) particles. The presence of the particles induces a change in the equilibrium shape and a shift of the prolate-oblate transition in the vesicle phase diagram, which are calculated within the framework of the spontaneous curvature model. As a consequence of the special form of the energy contribution due to the rods, these changes cannot be accounted for by a simple rescaling of the elastic constants of the vesicle as for solutions of spherical colloids or polymers.