Roger will probably reply also, but I'll give a bit.
Am I correct that your Rankin M was the one who married Nelly Hart 5 November 1839 in Henry County, TN? At least I have one of their children as being Ebenezer Polk, who, per my best efforts, appears to have been born in Henry County in 1845.
The YDNA tests won't likely ever be able to distinguish between whether Oliver is the son of James or the son of John, if the John to whom you refer was James's brother John. Some people even claim that Jacob was Oliver's father, not his grandfather. The descendants having their DNA tested and submitting the ancestral data on our site believe, from the paper evidence they have found, that Oliver's father was James.
This family is definitely closely related to the family that records show to be Scots-Irish; however, there is no evidence that Oliver's family migrated to the colonies with their relatives and may have lived in England for several generations before migrating.
I am not related to this family but have done research in Henry County, TN, and knew one of the descendants who had his DNA tested.