The statistical properties of the nonnuclear X-ray point sources from the ROSAT HRI survey of nearby galaxies in Paper I are studied, with particular attention to the contamination from background and/or foreground objects. This study reveals a statistical preference for the ultraluminous X-ray sources (ULXs) to occur in late-type galaxies over early-type galaxies, and in starburst/H (II) galaxies over nonstarburst galaxies. There is a trend of greater occurrence frequencies and ULX rates for galaxies with increasing star formation rates, confirming the connection between the ULX phenomenon and the star formation. A nonlinear correlation is found between the number of ULXs and the star formation rate, with significantly more ULXs at low star formation rates than the ULX population expected from the high-mass X-ray binaries (HMXBs) as an indicator of the star formation and the accompanying young stellar population, suggestive of another population of ULXs associated with the low-mass X-ray binaries (LMXBs) and the old stellar population. There are no breaks around 10(39) ergs s(-1) in the luminosity functions of ULXs in all galaxies or in late-type galaxies, suggesting the regular ULXs below 10(40) ergs s(-1) are a high-luminosity extension of the ordinary HMXB/LMXB populations below 10(39) ergs s(-1). There is evidence that the extreme ULXs above 10(40) ergs s(-1) might be a different ULX class from the regular ULXs below 10(40) ergs s(-1), although a larger sample with more ULXs is needed to establish the statistical properties of the extreme ULXs as a class.