A model 3D colloidal fluid of moderately nonspherical axisymmetric molecules interacting through a two-site Yukawa potential has been studied in planar Couette flow by the Brownian dynamics simulation method. It is shown that these fluids exhibit nonlinear rheological behavior. Shear thinning, normal stress effects and shear-induced alignment are reported and analyzed. The influence of the one-particle diffusion tensor on the rheological and orientational properties is discussed. The shear viscosities are lower for rods that diffuse with an anisotropic diffusion tensor.