Does an oath taken in a dream, from which one awoke before completing it, then fulfilled that oath, become binding?

A dream does not necessitate anything. If someone swears to do something while asleep, they are not obligated to fulfill it or offer expiation for it, because the sleeping person is not held accountable. This is based on the Prophet's (peace be upon him) saying: "The pen has been lifted from three: from the insane person until he regains his sanity, from the sleeper until he awakens, and from the child until he reaches puberty."