O'Dea made his MLB debut with the Chicago Cubs on April 21, 1935, at the age of 22. O'Dea performed respectably for the Cubs, serving as a backup catcher to future Baseball Hall of Fame member, Gabby Hartnett. When Hartnett was injured in 1936, O'Dea filled in with solid defensive play as well as hitting for a .307 batting average in 80 games. In 1937, he hit for a .301 average in 83 games. On December 6, , the Cubs traded him along with Frank Demaree and Billy Jurges to the New York Giants for Dick Bartell, Hank Leiber and catcher Gus Mancuso. With the Giants, O'Dea would once again be forced into a substitute role, as he backed up four-time All-Star Harry Danning. After three seasons with the Giants, he was traded on December 11, along with Bill Lohrman and Johnny McCarthy to the St. Louis Cardinals for Johnny Mize. The Cardinals also had an All-Star catcher in Walker Cooper, so O'Dea once again found himself in a back up role.