The relationship between the Liquid structures, vibrational interactions, and the wavenumber differences among the infrared (IR), isotropic Raman, and anisotropic Raman components of vibrational bands (the noncoincidence effect) is analyzed theoretically for the OH stretching bands of neat liquid methanol and a methanol-LiCl solution. The analysis is also carried out for the CO stretching band of neat liquid methanol for comparison. The IR and Raman spectra are calculated on the basis of the transition dipole coupling (TDC) mechanism and the liquid structures derived from molecular dynamics (MD) simulations (the MD/TDC method). It is shown that the signs and magnitudes of the noncoincidence effect observed for the OH and CO stretching bands of liquid methanol, which are significantly different between these two bands, are well reproduced by the calculations based on the same set of liquid structures and the same mechanism of vibrational interactions. The analysis of the origin of the noncoincidence effect shows that the vibrational interactions within hydrogen-bonded chains explain the major part of the noncoincidence effect for the OH stretching band of liquid methanol, while in the case of the CO stretching band, the negative noncoincidence effect arising from the vibrational interactions between hydrogen-bonded molecules is partially canceled by the contribution of the interactions between molecules which are not directly hydrogen bonded to each other. The reversed (negative) noncoincidence effect observed for the OH stretching band of a methanol-LiCl solution is shown to be mainly explained by the liquid structures formed around the Cl-ion and the vibrational interactions determined by the TDC mechanism. To support the discussion, ab initio molecular orbital (MO) calculations are performed for cluster species consisting of a Cl- or Li+ ion and a few methanol molecules. As an extension of the study on the methanol-Cl- system, ab initio MO calculations are also carried out for clusters with an electron substituted for the Cl- ion. A possible vibrational spectroscopic feature of the liquid structures formed around a solvated electron is discussed.