We investigate the motion of ferromagnetic nanowires confined to nanometer-scale oil films at an air/aqueous interface in response to the application of external magnetic fields and field gradients. By varying the oil viscosity, film thickness, and wire length, we cover two regimes of response suggested by theory: one where the surface viscosity is expected to dominate the wire's motion and one where the subphase viscosity is expected to dominate [Levine, A. J.; Liverpool, T. B.; MacKintosh, F. C. Phys. Rev. E 2004, 69, 021503]. For wire motion parallel to the long axis of the wire, the observed drag agrees reasonably with theoretical predictions. However, the drag on wires moving perpendicular to their long axis or rotating about a short axis is unexpectedly insensitive to the film properties over the full range of measurements. This behavior is in contrast to the rotational and translational drag on nanowires in molecularly thin protein layers, which follow theoretical expectations. The observations in the oil films, which are explained in terms of the manner in which the wire immerses dynamically in the film and subphase, demonstrate how the effective drag viscosity of an aspherical particle confined to a fluid interface can depend on its direction of motion.