The oscillation of a levitated drop is a widely used technique for the measurement of the surface tension and viscosity of liquids. Analyses are mainly based on theories developed in the nineteenth century for surface tension driven oscillations of a spherical, force-free, liquid drop. However, a complete analysis with both analytical and numerical approaches to study the damped oscillations of a viscous liquid drop remains challenging. We first propose in this work an extension of the theory that includes the coupled effects of surface tension and viscosity. The analytical solution permits derivation of both properties simultaneously, which is of interest for fluid with unknown viscosity. Then, the robustness of an Eulerian framework to simulate the fluid flow is discussed. Simulations of different oscillations modes for a liquid iron droplet immersed in a low density gas and comparisons with the derived theory are detailed and presented.