A theoretical model Hamiltonian [J. Chem. Phys. 2013, 138, 064308] for describing vibrational spectra associated with the CH stretch of CH2 groups is extended to molecules containing methyl and methoxy groups. Results are compared to the infrared (IR) spectroscopy of four molecules studied under supersonic expansion cooling in gas phase conditions. The molecules include 1,1-diphenylethane (DPE), 1,1-diphenylpropane (DPP), 2-methoxyphenol (guaiacol), and 1,3-dimethoxy-2-hydroxybenzene (syringol). Transforming the bending normal mode vibrations of CH3 groups to local scissor vibrations leads to model Hamiltonians which share many features present in our model Hamiltonian for the stretching vibrations of CH2 Fermi coupled to scissor modes. The central difference arises from the greater scissor-scissor coupling present in the CH3 case. Comparing anharmonic couplings between these modes and the stretch-bend Fermi coupling for a variety of systems, it is observed that the anharmonic couplings are robust; their values are similar for the four molecules studied as well as for ethane and methanol. Similar results are obtained with both density functional theory and coupled-cluster calculations. This robustness suggests a new parametrization of the model Hamiltonian that reduces the number of fitting parameters. In contrast, the harmonic contributions to the Hamiltonian vary substantially between the molecules leading to important changes in the spectra. The resulting Hamiltonian predicts most of the major spectral features considered in this study and provides insights into mode mixing and the consequences of the mixing on dynamical processes that follow ultrafast CH stretch excitation.