Otway was born in Wiltshire. He was educated at Sedbergh School and later consecrated Bishop of Killala and Achonry on 29 January 1671. He was translated to Ossory on 7 February 1680. From 1680 until 1691 he was also Archdeacon of Armagh in commendam. He died on 6 March 1692 in Kilkenny.
- Fryde, E. B.; Greenway, D. E.; Porter, S.; Roy, I. (1986). Handbook of British Chronology (Third Edition ed.). Cambridge, England: Cambridge University Press. p. 345. ISBN 0-521-56350-X.
- Cotton, Henry (1850). The Succession of the Prelates and Members of the Cathedral Bodies of Ireland. Fasti ecclesiae Hiberniae. Vol. 4, The Province of Connaught. Dublin: Hodges and Smith. pp. 67–78.
- Moody, T. W.; Martin, F. X.; Byrne, F. J., eds. (1984), Maps, Genealogies, Lists: A Companion to Irish History, Part II, New History of Ireland: Volume XI, Oxford: Oxford University Press, pp. 316–318, ISBN 0-19-821745-5
- "Fasti Ecclesiae Hibernicae: The succession of the prelates Volume 3" Cotton, H. p. 46. Dublin, Hodges & Smith, 1848–1878.
- “Fasti Ecclesiae Hibernicae: The succession of the Prelates- Volume 1” Cotton, H. 282: Dublin, Hodges, 1848.