Similar size and shape molecules with different electric multipoles are used to investigate effects of molecular dipole, quadrupole, and polarizability interactions on the average orientational order of solutes in nematic liquid crystals. Solutes are codissolved in the same sample tube so that the orientational ordering among solutes can be directly compared and analyzed using mean-field models. Permanent dipoles have a negligible influence on solute orientational order. Effects from molecular polarizability interactions could not be separated from short-range interactions. However, order parameters predicted from strong, short-range repulsive forces coupled with interactions between the solute quadrupole and the average electric field gradient felt by the solute are consistent with experimental values. For the nematic mixture 55 wt% ZLI 1132 in EBBA [N-(pethoxybenzylidene)-p'-n-butylaniline] the contribution to solute ordering from long-range electrostatic interactions is negligible.