He was educated at a local school and at Queen"s College, Galway.
He was called to the Irish bar in 1894 and became a Knights of Columbus (King’s Counsel) in 1913. Muldoon was a treasurer of the United Irish League and a Director of the Freeman"s Journal. In July 1907 he was elected unopposed at a by-election for East Wicklow, and was re-elected at both general elections of 1910, unopposed in January 1910 and by almost two to one over a Unionist in the December 1910 election.
In July 1911 he resigned and stood for the East Cork seat of fellow Nationalist Captain A. J. C. Donelan, who had been unseated following an election petition, having defeated William O"Brien the previous December.
Donelan succeeded Muldoon unopposed in East Wicklow, while Muldoon was in the event returned unopposed in East Cork. Muldoon was politically very active from 1900-1914.
His particular interests were the Local Government (Ireland) Acting 1898, the Land Acts and the Labourers (Ireland) Acting 1906, on all of which he published a number of works. He was a close political confidant of John Dillon, while said to be close to John Redmond and Joseph Devlin.
Muldoon retired from politics at the general election of 1918.
In 1921 he was appointed Registrar in Lunacy and five years later, after the establishment of the Irish Free State, as Registrar in the office of the Chief Justice of Ireland, retiring in 1935.
He was returned unopposed as Member of Parliament for the Irish Parliamentary Party in North Donegal at a by-election in June 1905 but did not stand again at the general election of January 1906, being deselected by the local clergy.
27th United Kingdom Parliament. 28th United Kingdom Parliament. 29th United Kingdom Parliament.
30th United Kingdom Parliament]
He was a Member of Parliament (Member of Parliament) for most of the period between 1905 and 1918, representing three different constituencies in the House of Commons of the United Kingdom of Great Britain and Ireland.