The static hyperpolarizabilities, oscillator-strength-distribution moments S₋₃ and polarizabilities for S-, P- and D-series of helium and alkali atoms in Rydberg states with principal quantum numbers n between 30 and 70 were calculated in the single-electron Fues' model potential approach. On the basis of the numerical data, three-term polynomials in powers of the effective principal quantum number have been proposed for rapid and accurate evaluations of the indicated characteristics for atoms in arbitrary highly excited states. Numerical values of the fourth-order coefficients in the field-power-series expansions for energies of S_1/2-, P_1/2,3/2- and D_3/2,5/2-states were determined in satisfactory agreement with available data of experiments and theory for rubidium atoms. The numerical data for sodium atoms were used for evaluating the second-order and fourth-order contributions to the electric field magnitude which can tune into double resonance the two-photon transitions between Stark sublevels of the nP_J- and - states via the (n + 1)S_1/2-state.