Hodges was born in Harpers Ferry, West Virginia to Joseph Howard and Edna Belle Hodges. He and his family later moved to Martinsburg, where he attended St. Joseph's High School. After graduating from St. Joseph's in 1928, he studied at St. Charles College, Catonsville, Maryland. He was then sent to further his studies at the Pontifical North American College in Rome. He was ordained to the priesthood in Rome on December 8, 1935. Following his return to the United States, he was attached to the Diocese of Richmond, Virginia, and served as a curate at . He served at before becoming director of the diocesan mission band. He was named pastor of in 1955. On August 8, 1952, Hodges was appointed Auxiliary Bishop of Richmond and Titular Bishop of Rusadus by Pope Pius XII. He received his episcopalconsecration on the following October 15 from Bishop Peter Leo Ireton, with Bishops Vincent Stanislaus Waters and John Francis Dearden serving as co-consecrators. In addition to his episcopal duties, he continued to served as pastor of St. Peter's Church. Returning to his native West Virginia, he was named Coadjutor Bishop of Wheeling on May 31, 1961. Upon the death of Archbishop John Joseph Swint, Hodges succeeded him as the fifth Bishop of Wheeling on November 23, 1962. Hodges attended all four sessions of the Second Vatican Council between 1962 and 1965. He dedicated much of his administration to implementing the reforms of the Council in the diocese, establishing a Liturgical Commission, Priests' Senate, Sisters' Council, and Cursillo movement. A strong supporter of ecumenism, he established a Commission for Religious Unity in 1964, co-founded the Joint Commission of Roman Catholics and Episcopalians in 1978 with the Episcopal Bishop of West Virginia, and joined the in 1981. He mandated parish councils in 1968, introduced extraordinary ministers in 1970 and permanent deacons in 1975, and renovated the exterior and interior of St. Joseph's Cathedral in 1973. The diocese was renamed as the Diocese of Wheeling-Charleston on August 21, 1974. In 1976, he established the Diocesan Pro-Life Office and led a public protest against the opening of a Wheeling abortion clinic. Hodges was also known as a social reformer, using his office to challenge the social, economic, and political injustice in Appalachia. He publicly supported the civil rights movement, urged local parishes to begin social outreach programs, and established such social ministry programs as soup kitchens and elderly-assistance programs. He served as chairman of the USCCBAd Hoc Committee for the Campaign for Human Development.