She was born in India. She grew up in Bombay and then Calcutta, raised by her grandmother--who she thought was her mother--in poverty. A 17 she and her "mother" moved to Britain and she began working unbilled in films. Eventually she met, became involved with, and eventually married Alexander Korda, who was 18 years her senior.
In the early 30s she worked in British films, then came to Hollywood.
Throughout her life, Oberon maintained she was born in Tasmania, Australia. She hid her father's parentage (Irish) and her mother's (Ceylonese, now Sri Lanka). In Britain, when living with her grandmother, she often pretended her grandmother was her maid, probably because the older woman was dark-skinned (relative to Merle).
She worked steadily in Hollywood throughout the 1940s, and into the 1950s, when work slowed down. Some films and TV followed in the 60s and 70s, but essentially she retired after 1954's Desiree.
Sadly, the fact that she hid her background behind fairy tales (lies) is not surprising, given the times and the fact that she was struggling to become a legitimate--or respectable--actress. Many actresses of the 19th and early 20th century did the same, including Sarah Bernhardt.