We present analytical calculations of the electronic spin-orbit interaction contribution to nuclear magnetic shielding tensors using linear and quadratic response theory. The effects of the Fermi contact and the spin-dipole interactions with both the one- and two-electron spin-orbit Hamiltonians, included as first-order perturbations, are studied for the H2X (X=O, S, Se, and Te), HX (X=F, Cl, Br, and I), and CH3X (X=F, Cl, Br, and I) systems using nonrelativistic multiconfiguration self-consistent field reference states. We also present the first correlated study of the spin-orbit-induced contributions to shielding tensors arising from the magnetic field dependence of the spin-orbit Hamiltonian. While the terms usually considered are formally calculated using third-order perturbation theory, the magnetic-field dependent spin-orbit Hamiltonian requires a second-order calculation only. For the hydrogen chalcogenides, we show that contributions often neglected in studies of spin-orbit effects on nuclear shieldings, the spin-dipole coupling mechanism and the coupling of the two-electron spin-orbit Hamiltonian to the Fermi-contact operator, are important for the spin-orbit effect on the heavy-atom shielding, adding up to about half the value of the one-electron spin-orbit interaction with the Fermi-contact contribution. Whereas the second-order spin-orbit-induced shieldings of light ligands are small, the effect is larger for the heavy nuclei themselves and of opposite sign compared to the third-order contribution.