This work is motivated by experimental and theoretical results on medial entorhinal cortex layer II stellate cells (SCs) in which persistent sodium and h-currents have been shown to be responsible for the generation of subthreshold oscillations in the theta frequency band. We use modeling, dynamical systems tools and numerical simulations to investigate the mechanisms underlying the subthreshold frequency response of SCs to oscillatory inputs and their consequences for the selection of preferred frequency responses to oscillatory inputs in both the sub- and supra-threshold voltage regimes. Previous theoretical work has used linear models. We incorporate the role of nonlinearities and time-scale separation between the participating ionic currents present in the model in determining the cell's voltage response to oscillatory inputs. We explain the dynamic mechanisms of attenuation of the voltage response to oscillatory inputs at both low and high-frequencies that give rise to the intermediate, resonant frequency band. These two mechanisms result from qualitatively different constraints on the speed and direction of the trajectory in phase-space imposed by the displacement of the voltage nullcline due to the oscillatory forcing. The nonlinearities present in the model are able to produce an additional amplification of the voltage response and a decrease in the resonant frequency as compared to the corresponding linearized model. Importantly, these nonlinear effects are observable when the time-scales of the voltage and h-current gating variables are well separated and, for constant input amplitudes, decrease as the level of time-scale separation decreases. In the latter cases, the nonlinearites are "ignored" and the voltage response approaches that of the linearized model. For low enough supra-threshold input amplitudes, the sub-threshold resonant frequency is communicated to the spiking regime. However, for higher input amplitudes, the firing frequency has additional peaks at higher frequencies. These patterns are qualitatively different from the analogous ones observed in the corresponding linearized systems. The principles extracted from our results are valid for a more general class of models including other types of ionic currents such as M-currents, and have implications for the response of cells to conductance-based oscillatory inputs.