There is a strong Oliver line in my family tree via marriage. My great grandfather's brother, Dr. Robert Wiley Rea (36th MS) was married to Rilla Elizabeth Oliver. Their beautiful home in Wesson, MS still stands today and remains in the family.
Her father was Captain William Oliver (1829-1891), one of the owners of Mississippi Mills in Wesson. In the late 1800's it was one of the largest cotton and woolen mills in the south, employing up to 2000 people at it's peak. My great grandfather James S. Rea was the Sec. & Treasurer of the company. The mill closed about 1910.
I've followed this Oliver line (using FamilySearch.org) for 9 generations thru MS, GA, NC, VA, to Cornwall, England. Sorry to say no tie to Cornelius or his father John Wesley that I could find.