O'Callahan was born on May 14, 1905, in the Roxbury neighborhood of Boston, Massachusetts. He joined the Society of Jesus (Jesuits) in 1922, shortly after graduating from Boston College High School. He began the 13 years of training required of a Jesuit at St. Andrew's College, Poughkeepsie, New York, where he received the Bachelor of Arts degree in 1925 and his Master of Arts degree in 1929, specializing in mathematics and physics in addition to religious philosophy. He was ordained to the Roman Catholic priesthood as a member of the Jesuit order in 1934. He was a Professor of Mathematics, Philosophy, and Physics at Boston College from 1927 to 1937. He then spent a year (1937–1938) as a Professor of Philosophy at Weston Jesuit School of Theology (Weston College). He served as the Director