In Chapter 3 of Things Fall Apart, Achebe writes:
Unoka was an ill-fated man. He had a bad chi or personal god, and evil fortune followed him to the grave, or rather to his death, for he had no grave. He died of the swelling which was an abomination to the earth goddess...He was carried to the Evil Forest and left to die.
So, the Ibo tribe has a way of explaining both physical and supernatural causality using fate by way of chi instead of in terms of free will. In other words, Unoka was a lazy man and died a dishonorable death because of his chi, not expressly because of his choices. Unoka was pre-determined to be agbala, to have no titles, and to be buried in the Evil Forest.
A Westerner might look at it from another point-of-view: Unoka had free will because he chose to sing and tell stories and not work. Unoka chose not to attain titles because he did not accept the culture into which he was born. So, his agbala status and dishonorable death are the result of his rebellion and not due to supernatural causes of chi or fate.
Okonkwo attempts to determine his own fate. Knowing his father was a failure, he works the yam fields twice as hard to compensate. However, Okonwko is also a character in a tragedy, both personal and cultural (both he and his tribe will "fall apart" and die). In tragedies, characters are engineered for downfall. Obviously, as a character, Okonwko has no control over his and his tribe's death. Yet, Okonkwo fights to the death, regardless. So, in a way, he chooses his fate by beheading the messenger. He chooses to be placed in a situation which allows him to be aggressive and violent so as to cause his own self-destruction by violent means (suicide).
So, overall, I would say that characters in a tragedy do not have free will, even though they ironically fight to the death in order to preserve it. In tragedy, tragic heroes are victims of tragic fate, which is a combination of outside determinism and bad personal choices. Okonkwo's death is foreshadowed early and often so as to create dramatic irony, the principle device which guides all tragedy.