Oram was born in 1885 at Christchurch. His mother was May Eltham, originally from Hobart in Tasmania. His father, Matthew Henry Oram, died three months before Matthew Oram's birth. His formal education started at age 12, as he went to live with his aunt in Wellington after his mother's death. He attended Wellington College (1898–1904), followed by Victoria University of Wellington (1905–1911). He graduated BA (1908) and received a Sir George Grey Scholarship (he came equal in the examinations with Miss Barkas, but as she had also won and accepted another scholarship, Oram was given the Sir George Grey Scholarship), and then graduated MA (Hons) (maths and physics, 1909) and LLB (1912). During his education, he competed in athletics. He belonged to Victoria's debating society and won prizes (Plunket Medal for Oratory and the Joint Challenge Scroll and Union Prize). He was also a member of the Territorial Force.