A theory recently proposed characterizes effective two-body interactions in gases by molecular sizes and energies plus effective measures of the nonconformality between the exact potential and a spherical reference. This theory provides a procedure to construct effective potentials which reproduce the second virial coefficients B(T) of the substance of interest and allows us to express B(T) in simple and compact form. In this paper we test the applicability of the theory to a variety of nonspherical models-spherocylinders, ellipsoids, Lennard-Jones polyatomics, square-well chains, and Stockmayer molecules-and show that their virial coefficients are accounted for accurately by the theory. The theory is used to study the effects of molecular geometry, particularly the elongation of linear molecules, on the angle averaged molecular parameters and on the effective potential. The effective potentials of the models considered are obtained, and the effects of size and geometrical shape are discussed.