Monte Carlo results for both spherical and nonspherical electrorheological (ER) particles are described. The ER particles are modeled as hard spheres or hard ellipsoids of revolution with much smaller charged hard spheres (ions) constrained to their inner surface. NVT Monte Carlo calculations show that these models display the strong polarization and chain formation characteristic of ER fluids. Both prolate and oblate ER particles align with their longest axis directed along the applied field allowing for larger induced dipole moments than those obtained for spherical ER particles of equal volume. In all cases it is found that chaining occurs at relatively high fields where the induced dipole moments are approaching their maximum value. An interesting feature of nonspherical ER particles is the field-induced orientational order. It is found that even slightly nonspherical ER particles are highly ordered by fields which are weaker than those required to induce chain formation. Very weak fields are sufficient to generate strong orientational order in prolate ER particles with moderate aspect ratios. Further, field-ordered oblate ER particles tend to align their symmetry (short) axes to form a biaxial phase at high densities. The field-induced, liquid-crystal-like behavior of nonspherical ER particles is discussed in detail.