Assuming that the polarizability is a linear function of the nuclear coordinate, i.e., alpha(q) = alpha(0) + alpha(1)q, we obtain analytical expressions of the (2n + 1)th-order signals and show that the leading order of the signals (n>1) is proportional to g(n+1), where g(n+1) is the coefficient of the anharmonic potential V(q) = g(3)q(3)/3! + g(4)q(4)/4!+.... In Other words, detection of the (2n + 1)th-order signal implies the direct observation of the (n + 1)th-order anharmonicity within the approximation. Based on this fact we discuss a possibility to detect the (n + 1)th-order anharmonicity directly from the (2n + 1)th-order experiment. Calculations are made by using novel Feynman rules for the nonequilibrium multitime correlation functions relevant to the higher-order off-resonant spectroscopy. The rules have been developed by the authors and are presented compactly in this paper. With the help of a conventional double-sided Feynman diagram, we draw physical pictures of higher-order off-resonant optical processes. Representative calculations for CHCl3 of the fifth-, seventh-, and ninth-order optical processes are presented and discussed.