The electric field gradient (EFG) at the nuclei, the generalized Sternheimer shielding constants and the EFG electric dipole polarizabilities are computed for eight small molecules employing multiconfigurational self-consistent field wave functions and the corresponding linear and quadratic response functions. The molecules studied are H-2, N-2, CO, HF, C2H2, HCl, HCN, and HNC, all of which are linear. For the hydrogen molecule, full configuration-interaction results for the properties are also reported. The dependence of the computed quantities on the basis set and the electron-correlation treatment is analyzed.