The Blue Line is the subway to O'Hare. In the downtown area it runs as a subway under Milwaukee Avenue, Lake Street, Dearborn Street and Congress Parkway. In outlying areas it runs on elevated structure and in expressway medians. The line into O'Hare was completed in 1984 and enters the airport via the median of I-190 and a short subway.
You are correct, the Clinton station on the Blue Line is two blocks south of Chicago Union Station. No extension has been planned to run the Blue Line directly to Union Station -- most people don't see the need for a two-block subway route. Years ago, before the Congress subway was built and 'L' trains ran on the old Metropolitan West Side Elevated, there was a somewhat closer station at Canal one-half block south of Jackson Boulevard, but when the subway was constructed in 1958, beneath Congress Parkway was chosen as the most practical routing.
The Orange Line station closest to Chicago Union Station is at Quincy/Wells, which is about four blocks east of Union Station. Be sure you enter the 'L' station on the east side of Wells Street, as the Orange Line only stops on that side. The Orange Line runs clockwise around the Loop, so if you are going from Union Station to Midway you will travel around the Loop over Wells Street, Lake Street and Wabash Avenue before heading southwest to the airport.