While the idea of jinn (also spelled djinn or genie) possession seems bizarre to many people, it is actually common in many parts of the world, including Pakistan, where the family was from.
Jinn are described in the Koran, the Muslim holy book, as creatures made by Allah of smokeless fire. There are parallels between Christian angels and Muslim jinn, and many Muslims believe in the literal existence of jinn, just as many Christians believe in the literal existence of angels. Both can and do interfere with the affairs of mankind (sometimes for good or ill), though in Christian theology it is typically demons - not angels - that possess humans.
In his book Legends of the "Fire Spirits: Jinn and Genies from Arabia to Zanzibar," scholar Robert Lebling writes, "In the Islamic world the belief is fairly widespread that jinn can possess humans, speak through them and direct their behavior. Like their demon analogues in Christianity, they can also be exorcised through rituals. ....Today, jinn possession is taken quite seriously in a number of Arab countries, including Saudi Arabia, where [revered Muslim scholar] Sheikh Abdul Aziz bin Baz... wrote about his own participation in numerous exorcism rituals."