The effect of external electrostatic fields on the spherical oscillator energy states was studied using stationary perturbation theory. Besides the spherical oscillator with ideal symmetry, also a variety of the deformed systems were considered in which the deformations may be induced by the external fields, but also by the short-range crystal lattice forces. The perturbation theory analysis was carried out using the field-dependent basis functions. Predicted spectral appearances and band splittings due to the deformations and external field influences were shown to be helpful in interpreting the experimental spectra of molecular oscillator possessing subsets of mutually orthogonal triply degenerate normal modes (such as, e.g. tetrahedral species). To verify the results of the perturbation theory treatments, as well as to provide a further illustration of the usefulness of the employed technique, a numerical HF/aug-cc-pVTZ study of the vibrational states of methane molecule in external electrostatic field was performed.