Éliás Methód Gojdics came from a long line of Greek Catholic priests. He completed his studies at the Greek Catholic Theological Institute in Eperjes and was ordained a priest on December 6, 1896. He was a married priest; his wife was Mária Happel. After serving in Hungary, he was already working in the United States in 1903 as pastor to the Greek Catholic congregation in Bayonne, New Jersey. The Eperjes sematismus listed him at this time as a member of the episcopal curia.

At the end of 1904, he became the pastor of the Greek Catholic community in Bridgeport, Connecticut. He was the parish’s first priest to devote his full time to serving the community. Initially, he held services in the basement of a Latin Rite Catholic church. During his tenure, the decision was made to build a church of their own, and on December 5, 1905, with his assistance, the St. John the Baptist Church parish was officially registered. In 1906, the basement section of the church was completed. He served in Bridgeport until 1908.

By 1924 at the latest, he was the pastor of St. Michael Byzantine Catholic Church in Farrell, Pennsylvania. Under his leadership, the church was rebuilt and expanded in March 1924, and Bishop Basil Takach reconsecrated it on September 27, 1928. Gojdics died in Farrell on February 25, 1931. He was buried at the nearby Hermitage Saint Michael Byzantine Catholic Cemetery.