A general theory for the dynamics of aspherical droplets useful to interpret frequency spectra more accurately for thermophysical property measurements was developed. The oscillations of a non-spherical droplet oscillating about an oblate spheroid subjected to external forces are considered. The effect of the static deformation and the interaction between the drop oscillation and the external field on the resonance are investigated. The analysis developed can be extended to consider different static shape deformation shapes. In order to validate the analytical predictions and to conduct further investigations, an experimental apparatus and a novel experimental procedure were developed. Experimental data and observations on the frequency splitting and surface tension, and the dynamics of the droplet in the experimental apparatus are presented. Finally, the effect of fullerenes on some dynamic features of levitated droplets is investigated.