Joseph Ogola Olita was born on March 31, 1944 to mother Regina Oduma. In 1951, Olita attended Pap Oriang Primary School. In 1958, he enrolled at St. Mary's Yala where he went for his O level and was an active drama club member.

After completing his secondary education, Olita was an employee of the Brooke Bond Company in Kericho and the Union Carbide in Nakuru. Olita was a deeply spiritual man having attended Barding Secondary School, between 1956 and 1960, and later proceeded to Yala Seminary School. Olita was working for USAID when the opportunity to act in 1981's Rise and Fall of Idi Amin presented itself

According to NTV Uganda, Olita did not know much about Amin, so he "read a lot about him through books, through newspapers and the clips." He missed the chance to act as him when he was approached to portray the role in the 1976 film, Victory at Entebbe. When it came time to portray him in Rise and Fall, "I really had to master his mannerisms." Rise and Fall of Idi Amin won five awards, including Best Actor, at the Las Vegas International Film Festival. Olita not receiving an Oscar nomination for his performance has been considered one of the worst acting snubs in the history of the Academy Awards. "You see these wazungu are so selfish. They just wanted to make one of their own a star. (Forest) Whitaker’s performance and role in The Last King of Scotland is nowhere close to what I did and still able to do," says Olita.

In 1984, Olita portrayed the minor role of the First Policeman in Sheena. In 1991, he reprised his role as Amin for the second and final time in Mississippi Masala which also starred Denzel Washington. Olita also portrayed an army general in The Black Forest Clinic.

Olita's final screen appearance was in the 2011 romantic comedy, The Captain of Nakara, in which he portrayed Muntu’s father-law.