Irvington is a home rule-class city in Breckinridge County, Kentucky, in the United States. The population was 1,181 at the 2010 census. Irvingto…Irvington is a home rule-class city in Breckinridge County, Kentucky, in the United States. The population was 1,181 at the 2010 census. Irvington is located at 37°52′44″N 86°17′5″W / 37.87889°N 86.28472°W.