There are 6 US Post Offices in Union County serving a total of 24,956 residents equating to 4,159 residents per post office. It's estimated that approximately 39,833 packages are handled across the 6 county post offices annually. Union County is a county located in the U.S. state of Oregon. As of the 2010 census, the population was 25,748. Its county seat is La Grande. Union County comprises the La Grande, OR Micropolitan Statistical Area. It is one of the eight counties of eastern Oregon.