We have used time-resolved x-ray photoemission electron microscopy to investigate the magnetization dynamics induced by nanosecond current pulses in NiFe/Cu/Co nanostripes. A large tilt of the NiFe magnetization in the direction transverse to the stripe is observed during the pulses. We show that this effect cannot be quantitatively understood from the amplitude of the Oersted field and the shape anisotropy. High frequency oscillations observed at the onset of the pulses are attributed to precessional motion of the NiFe magnetization about the effective field. We discuss the possible origins of the large magnetization tilt and the potential implications of the static and dynamic effects of the Oersted field on current-induced domain wall motion in such stripes.