Odeh grew up as a refugee in Ramallah in the West Bank, which she saw come under occupation by the Israeli army in 1967.

When she was 21, in 1969, Odeh was arrested in the middle of the night by Israeli soldiers at her home, and for twenty-five days her interrogators tortured her. She was beaten from head to toe with sticks and metal bars; her body, including genitalia and breasts, was subjected to electric shocks after she was forced to watch a male prisoner tortured to death in this very way. All the while, she was told she would die if she did not confess. But it was not until they brought in her father, threatening to force him to rape her, that she agreed to sign a confession stating that she had helped orchestrate two explosions in West Jerusalem that killed two civilians. Even then, her torturers raped her with a thick wooden stick.

Standing before a military court less than one month later, Odeh renounced the confession. But the panel of judges ignored that, and Odeh was sentenced to ten years plus life in prison. Ten years later, she was released in a prisoner exchange, along with seventy-five other Palestinians. That same year, in 1979, Odeh traveled to Geneva, where she described to the United Nations precisely how she came to be convicted of terrorism by Israel. In the years following, Odeh lived in Lebanon and Jordan, where she obtained a law degree. In 1995 she immigrated to the United States, joining her brother and father, both US citizens, and the large Arab-American communities in Detroit and, later, Chicago.