The transient, collision-induced changes in electric properties of ion-atom or atom-atom pairs at long range are determined by the polarizabilities and hyperpolarizabilities of each of the interacting species. Induction effects on moments of the charge distribution or static susceptibilities depend on the response at zero frequency, and dispersion effects depend on the polarizabilities (linear and nonlinear) at imaginary frequencies. In this paper, we give numerical results for four static multipole hyperpolarizabilities of the helium atom obtained from large-basis, ab initio calculations using many-body perturbation theory and coupled-cluster methods. We report and analyze the numerical results for the R(-6) and R(-8) terms in the dispersion contributions to the He-He, He-H, and H-H pair polarizability functions with a corrected formula for the contributions form P-hyperpolarizability tensor. For both parallel and perpendicular components of the polarizability, the numerical results at order R(-8) have contributions of similar magnitude arising from the terms containing the P and Q hyperpolarizabilities; these terms approximately cancel for Delta alpha(perpendicular to), but reinforce for Delta alpha(parallel to). When R is near to or smaller than the van der Waals minimum distance, the dispersion series is damped by overlap, but the ratio of the undamped R(-6) and R(-8) terms gives a guide to the convergence behaviour. For the pairs treated here, the R(-6) and R(-8) terms in Delta alpha(parallel to) become equally important between 5 and 8 bohr, but the R(-6) term dominates the series for Delta alpha(perpendicular to) down to separations of 3-4.5 bohr.