The expressions for vibrational energy relaxation (VER) rates of polyatomic molecules in terms of equilibrium capacity time correlation functions (TCFs) derived in the first paper of this series [J. Chem. Phys. 110, 5273 (1999)] are used for the investigation of VER of azulene in carbon dioxide at low (3.2 MPa) and high (270 MPa) pressure. It is shown that for both cases the VER times evaluated on the basis of the same potential model via solute-solvent interaction capacity TCFs by means of equilibrium molecular dynamics (EMD) simulations satisfactorily agree with the nonequilibrium (NEMD) molecular dynamics [J. Chem. Phys. 110, 5286 (1999)] and experimental [J. Chem. Phys. 105, 3121 (1996)] results as well. Thus it follows that these methods can complement each other in characterizing VER from different points of view. Although more computational power and refined methods of dealing with simulated data are required for EMD simulations, they allow the use of powerful tools of equilibrium statistical mechanics for investigating the relaxation process. To this end, an analysis of VER mechanisms on the basis of normal mode and atomic representations is carried out. The influence of temperature and CO2 pressure on azulene normal mode spectra and solvent assisted intermode coupling in connection with the eigenvector structure is investigated in great detail. The normal mode capacity cross-correlation matrix reveals the significance of intermode coupling, which significantly contributes to intramolecular vibrational energy redistribution (IVR). As a new concept, partial normal mode relaxation rates are introduced. It is shown that these rates demonstrate similar properties as the energy exchange rates through particular normal modes in nonequilibrium simulations. Atomic spectra and friction coefficients are characterized by a complicated frequency dependence due to contributions from many normal modes. Atomic capacity TCFs and partial relaxation rates are analyzed and reveal a similar picture to that obtained from NEMD simulations. These results show that VER and IVR cannot be separated from each other and have to be considered as mutually connected processes.