This paper concludes a series of three papers presenting ROSAT High Resolution Imager (HRI) observations of unidentified Einstein and serendipitous ROSAT X-ray sources in the direction of the Magellanic Clouds. Accurate positions and fluxes have been measured for these sources. Optical photometry and spectroscopy were obtained to search for identifications in order to determine the physical nature of these sources. The present paper includes new data for 24 objects; identifications are given or confirmed for 30 sources. For six sources, optical finding charts showing the X-ray positions are provided. The results from this program are summarized, showing that the populations of luminous X-ray sources in the Magellanic Clouds are quite different from those in the Galaxy.