Is the wife still lawful for her husband after he uttered the oath of divorce four times without the intention of divorce, knowing that one of the times was in jest and another in a state of extreme anger, and they are still living together and have two children?

Perhaps the questioner does not differentiate between an oath of divorce and the pronouncement of divorce. Your statement to your wife, "You are divorced," is an immediate and effective divorce, even if you were joking or angry with an anger that did not deprive you of consciousness.

Therefore, the questioner must refer his case to the court to clarify the exact wording he used with his wife and the state he was in (joking, angry, serious), to determine whether his wife has become irrevocably separated from him or not.

The ruling in this case, whether it be a major irrevocable separation preventing continuation with the wife, or a ruling of no separation allowing them to remain together, depends on knowing the true nature of what transpired, and this can only be achieved by directly consulting a Mufti.