Oldham's father, Thomas, was professor of geology at Trinity College, Dublin, and director of the Geological Surveys of India and Ireland. Oldham, who was born in Dublin, was educated at the Royal School of Mines; in 1879 he followed his father in joining the Geological Survey of India, rising to the rank of superintendent. He retired in 1903 and became director of the Indian Museum in Calcutta.

Oldham made two fundamental discoveries. He made a detailed study of the Assam earthquake of 1897 and, in 1900, was the first to identify clearly the primary (P) and secondary (S) seismic waves transmitted through the Earth, which had been predicted by the mathematician Siméon Poisson on theoretical grounds. Secondly, in 1906 he provided the first clear evidence that the Earth had a central core. He found that the arrival of the primary, or compressional, waves was delayed at places opposite to the focal point of an earthquake. He deduced from this that the Earth contains a central core that is less dense and rigid than the rocks of the mantle, and through which compressional waves would travel less fast. A detailed analysis of the arrival and distortion of the P and S waves that had traveled through or near to the center of the Earth later provided much insight into the structure of the Earth.