Offa was born at Elsmore in 1888 to Alfred and Jessie Penberthy. He was a twenty-eight-year-old Station Manager when he enlisted at Armidale NSW in October 1916. He was one of a large group of recruits given a public farewell at Inverell Town Hall in October 1916 when they were all presented with the Inverell Medal and a pair of socks.
As a member of the 13th Battalion 23rd Reinforcement, he sailed from Australia for England on HMAT A72 Beltana in November 1916. After several months training at Codford his unit was sent to France in May 1917 where he was transferred to 13th Battalion 22nd Reinforcements. When he became ill with bronchitis in August 1917 he was sent to England for treatment, returning to his unit six months later. Just a few weeks later he was accidentally wounded in the thigh by a bomb and invalided to England again. He returned to Australia and was medically discharged in May 1919.
Not long after his return Offa married and became the Licensee of the Belmore Arms Hotel at Elsmore until its closure in 1928. He then moved to Sydney where he lived and worked until his death in 1953.