We report investigations of a pendant diluted crude-oil droplet in water that is forced to oscillate at a frequency omega. The droplet interface contains a significant amount of surface-active agents and displays a marked viscoelastic rheology with elastic moduli larger than viscous ones. At a low frequency, fluid viscosity and inertia are negligible, which allows a direct determination of the dilatational interface rheology. At a large frequency, eigenmodes of inertial shape oscillations are excited. By decomposing the interface shape into spherical harmonics, the resonance curves of the inertial modes of the interface are determined, as well as the frequency and damping rate of each mode. These two parameters are of major importance for the prediction of the deformation and breakup of a droplet in any unsteady flow without any prior knowledge of either the chemical composition or the detailed rheological properties of the interface. Then, interfacial rheology is related to interface dynamics by solving the coupled dynamic equations for the two fluids and the interface. It turns out that the rheology of the interface is well described by an equivalent two-dimensional viscoelastic material, the elasticities and viscosities of which depend upon the frequency. A first significant result is that shear and dilatational elasticities are closely connected, as are shear and dilatational viscosities. This implies that intrinsic rheology plays a major role and that compositional rheology is either negligible or strongly coupled to the intrinsic one. A second major result is that, for moderately aged droplets (<= 5000 s), the elasticity and viscosity at a high frequency (10-80 Hz) can be extrapolated from low-frequency measurements (<= 1 Hz) by a simple power law of the frequency, omega(z). The exponent z is related to the loss angle loss by a relation found in many previous low-frequency investigations of crude-oil interfaces: z = theta(loss)/2 pi. The present work thus extends classic observations obtained at a low frequency to a higher frequency range corresponding to the natural frequency of the droplets, where the droplet shape results from the balance between dynamic pressure and surface stresses and the interface involves simultaneous shear and dilatation. These results bring about serious constraints regarding the modeling of physicochemical underlying mechanisms and provide some insights for the understanding of the structure of crude-oil interfaces.