Sheridan came from Drumlish in County Longford, and had three brothers and two sisters. He moved to Westmeath, first to Kilbeggan and then to Mullingar. An auctioneer and farmer by profession, he was elected to Westmeath county council, and then to Seanad Éireann on the Agricultural Panel at a by-election on 14 May 1956. He was re-elected at the 1957 Seanad election, this time on the Labour Panel. He was elected to Dáil Éireann as an independent Teachta Dála (TD) for the Longford–Westmeath constituency at the 1961 general election. In spite of his Fine Gael background, he supported the minority Fianna Fáil government. He was re-elected at the 1965, 1969, 1973 and 1977 general elections. He concentrated on local constituency needs, with the electoral slogan "Vote for Joe, the Man you Know." He retired at the 1981 general election.
