He was educated at Seton Hall College and Immaculate Conception Seminary in South Orange, New Jersey, where he earned a Master of Arts degree in 1923.

[3] His younger brother, John L. McNulty, was ordained at the same liturgy (and later served as President of Seton Hall University from 1949 to 1959).

[3] He received his episcopal consecration on October 7, 1947, from Archbishop Thomas Walsh, with Bishops William A. Griffin and Henry Joseph O'Brien serving as co-consecrators.

[5] McNulty oversaw the implementation of the Decrees of Vatican II including the establishment of the Priests' Senate.

McNulty promoted religious vocations, expanded inner city ministry, established the Liturgical Commission, the Pastoral Council, a Lay Steering Committee to oversee finances, and the Communications Office.