They launched a lawsuit on Thursday against Fr Peter Miqueli, 53, who currently leads St Frances de Chantal church (pictured above) in the Throggs Neck area of the city.
The writ claims Mr Miqueli paid up to 1000 dollars a time to have gay sex sessions with a Mr Keith Crist, and paid $264,000 for a house in New Jersey.
It also claims he paid a doctor to obtain illegal drugs, and gave him $60,000 towards a house deposit.
Court papers say: "This lawsuit seeks to finally put an end to this truly sinful conduct so that St. Frances de Chantal parish can regain the strength, spirituality and faith it once had before Father Miqueli arrived."
Fr Peter Miqueli is yet to enter a response to the allegations against him and proceedings continue.
Churchgoers have also accused the Archdiocese of New York of knowing about Fr Miqueli's actions and doing nothing to stop them.
The Archdiocese denies this, and a statement on its website said: "The archdiocese has, from the beginning, taken these allegations seriously, and has been investigating them, including conducting a forensic audit of the parish, which is still on-going.
"To date we have found nothing to substantiate the allegations that have been raised, and, in fact, with regard to the parish finances, we know that the allegation that Father Miqueli stole $1 million from each parish, as was alleged by the plantiffs' attorney, is completely false.
"If anyone has information or documentation to substantiate the allegations, we would invite them to bring that information forward, or to contact the district attorney."