He then attended Yale Law School from 1939 until fall 1941, when he was drafted to serve in the United States Army.

After four years of military service during World War II, he returned to Yale and graduated with a Bachelor of Laws in 1946.

[2] After working as Justice Black's sole law clerk from 1946 to 1947, Oberdorfer went into private practice in Washington, D.C., with the firm Paul, Weiss, Wharton & Garrison as a tax attorney until his friend and law school classmate deputy attorney general Byron White asked him to join the United States Justice Department in 1961.

When Griffin Bell became attorney general in 1977, Oberdorfer was considered for the deputy position but was instead appointed to the federal bench.

As a judge, Oberdorfer opposed mandatory sentencing policies, especially with respect to drug offenders.