NULL Of 254 counties in the Lone Star State, Oldham County ranks 23rd by size (1,501 square miles). Oldham County is in Panhandle Texas. Recent listings of residential land and property for sale in Oldham County, Texas, totals around 1,000 acres and a combined market value of about $400,000. The most common type of land for sale by combined acreage in Oldham County is farms. Browse all residential property and land for sale in Oldham County to find residential land and properties that suit your lifestyle needs, from existing residential homes and estates to land ready for future residential-property development. The most common type of land for sale by combined acreage in Oldham County is farms.