There are 3 US Post Offices in Oldham County serving a total of 1,872 residents equating to 624 residents per post office. It's estimated that approximately 2,988 packages are handled across the 3 county post offices annually. Oldham County is a county located in the U.S. state of Texas. As of the 2010 census, its population was 2,052. Its county seat is Vega. The county was created in 1876 and organized in 1881. Oldham County is included in the Amarillo, TX Metropolitan Statistical Area."