You say Oliver is buried in a Gainsville cemetery, but you didn't include any dates for him.Here is the combined info from TX Dth Idx and SSDI:
Porter, Oliver H., b 22 Feb 1889; d 4 May 1970 Cooke Co, TX; last residence Gainsville, Cooke Co, TX; SS card issued in TX.
Looks like he might be too old to be a brother to Nancy.Is Nancy deceased?If so, have you obtained a copy of her death certificate?It should show the names of her parents.Accuracy only as good as the knowledge of the informant, but you can also obtain a copy of the application she filled out for her Soc Sec card, and it should show the names of her parents, her residence at the time she applied and other data, too.
An obituary might be helpful on this Oliver.Survivors are usually listed and you could see if your Nancy is on that list.
I don't find an Oliver Porter on the 1920 census that fits, but you could post a query asking for someone to do a 1930 census lookup for Nancy -- I don't have online access to that one.The Ancestry.com 1930 has an everyname index, not just head of household.