Is a wife considered irrevocably divorced after she has been divorced allusively once, explicitly another time, and a third time her husband uttered threatening words of divorce such as: "By Allah, I will divorce you," and "We are divorced," and "We have divorced, and there is nothing left between us," while intending not to effect an explicit divorce?

If you utter an ambiguous divorce statement (kinayah) without the intention of effecting a divorce, then no divorce occurs. The statement "By Allah, I will divorce you" is a promise that does not result in divorce. However, if you utter this oath while being aware and intending it as an oath, then you must offer expiation for an oath (kaffarat yamin (definition)) if you break it. As for the statement "We are divorced" and what follows it, if it is an initiation [of divorce], it is an effective divorce because it is explicit. If it is a false report, the preponderant opinion is that no divorce occurs by it. It is preferable to present these matters to trustworthy scholars.