Is expiation required of one who said, "By God, it's done," without intending anything specific, and then ate of another kind?

There is no expiation incumbent upon you, because you did not intend to swear an oath about eating. Rather, you intended one of two things: either to inform that you were full, or the oath merely slipped from your tongue without intention. This is the 'laghw al-yameen' (unintentional oath) which Allah has pardoned. Thus, there is no expiation for it, nor any sin, as Allah the Almighty says: "Allah will not impose blame upon you for what is unintentional in your oaths."