Podoley played for the Redskins from 1957 to 1960. In July 1961, he was involved in a three-team trade with the Redskins, Dallas Cowboys and New York Giants. The Giants received Podoley and end Joe Walton from the Redskins, the Redskins received Fred Dugan from the Cowboys and placekicker John Aveni, end Jerry Daniels, and defensive halfbackDave Whitsell from the Giants, and the Cowboys received placekicker Allen Green and a sixth round for the 1962 NFL draft from the Giants that the team later used to draft George Andrie.[1][2] However, Podoley retired instead.