They are related, but not the same, either in use or meaning.
'Oblivious' is an adjective, meaning out of consciousness, not remembered, not noticed. "He was oblivious to (completely unaware of) the fact that his plumbing had sprung a leak."
'Oblivion' is a noun with two meanings. 1) The condition of being unaware, which relates to the adjective's meaning. 2) The condition of being destroyed. "The forest faced oblivion when the logging company bought the land."