The infrared optical Kerr effect (IR-OKE) and two-color infrared pump-probe spectroscopies, which can be directly used to study intermolecular vibrational energy relaxation pathways, are theoretically studied. The IR-OKE method involves an intense IR pulse with controlled frequency to build up large population on a specific intramolecular vibrationally excited state. After a finite mixing time, which is also experimentally controlled, the time evolution of the nonequilibrium density matrix is detected by using the femtosecond optical Kerr effect measurement. Due to the nonequilibrium population distribution initially induced by the intensive infrared pulse, the measured OKE signal differs from that measured for a molecular system initially in thermal equilibrium state. Particularly, it is found that the deviation from the harmonic response can be specifically measured by using this method. By following the same procedure developed in this paper, the two-color IR pump-probe absorption spectroscopy is also considered and the corresponding nonequilibrium IR response function is theoretically investigated with a direct comparison with complementary IR-OKE response function. By using the perturbation theory, the corresponding response functions are obtained in terms of the molecular properties such as linear and nonlinear spatial derivatives of dipole and polarizability and cubic and quartic anharmonic coefficients. Also, it is emphasized that this method is conceptually quite similar to the transient nuclear Overhauser effect nuclear magnetic resonance spectroscopy.