This paper focuses on the dynamics of a domain wall (DW) displacing along an elliptically bent nanowire (NW) under the action of spin-polarized electric currents and external magnetic fields. Our results evidence that a curvature gradient induces an exchange-driven effective tangential field responsible for pinning a DW at the maximum curvature point in the NW. However, the competition between the torques produced by the external stimuli and the curvature-induced effective fields changes the DW equilibrium position and phase. Therefore, when the external stimuli are below a certain threshold, the DW follows a damped harmonic oscillation around the new equilibrium position. Above this threshold, DW displaces along the NW under an oscillatory translational motion.