Heron was born in Armagh, Ireland, the eldest of three sons born to Charles and Annie Heron. His father was the principal of St. Patrick's Boys School, while his mother headed the girls' section. The family lived in Banbrook Hill, and the 1911 census lists Oscar and his two brothers John and Charles, their parents, his mother's father Jeremiah McKenna, a cook, and two servant girls as residing there.
Heron served for a period in the Connaught Rangers, before being commissioned from cadet to temporary second lieutenant in the Royal Flying Corps on 13 December 1917. He was assigned to No. 70 Squadron to fly the Sopwith Camel single-seat fighter in May 1918. On 30 June, he gained his first victories, driving down an Albatros D.V and setting another ablaze. It would not be until 19 August that he would win again, when he destroyed a Fokker D.VII on an evening patrol. Again, there would be over a month's lapse, until he destroyed another Fokker D.VII on 28 September. On 1 October, Heron became an ace by destroying the only two-seater on his list; on the 7th he accounted for two more D.VII's, and three more on the 9th. For one of these, Heron cooperated with Captain Sydney Liversedge, Lieutenant Kenneth Watson and two other pilots to force down and capture a Fokker. Heron was appointed a flight commander with the temporary rank of captain on 23 October, going on to gain three more victories, two on 26 October, and his thirteenth and last on the 28th. In the end, besides the captured aircraft, Heron destroyed ten enemy machines and drove down two out of control. Heron was subsequently awarded the Distinguished Flying Cross, which was gazetted on 7 February 1919. His citation read: On 15 July 1919 Heron was granted permission to wear the Croix de guerre conferred by Belgium.
Heron was killed on 5 August 1933 while taking part in a mock aerial combat over Phoenix Park, Dublin, for Irish Aviation Day. Three days before, during practice flights, two aircraft collided, killing Lieutenant J. P. Twohig. Heron acted a pall-bearer at Twohig's funeral on the morning of the event. In the display Heron flew a Vickers Vespa, fighting off an attack by three Avro Cadets. At the end he made a low pass over the park, in front of a large crowd, including his wife, but span into the ground from a height of about. Heron and his air gunner were pulled from the wreckage, but he died almost immediately, while the air-gunner, Private Richard Tobin, died the following day. Heron was buried with full military honours at Glasnevin Cemetery on 8 August.