What is the religious ruling on a young man marrying a girl to whom he said in a moment of anger: "You are forbidden to me as a wife, and it would likewise be a religious prohibition if I were to marry you"?

Your statement to the girl, "You are forbidden to me as a wife," depends on your intention. If you intended it as an oath, then it is an oath, and you must offer expiation for an oath. If you intended it as zhihar (a pre-Islamic form of divorce by which a man declared his wife to be like his mother's back, thus making her unlawful to him), then it is zhihar, and it is not permissible for you to touch her – meaning to engage in sexual intercourse – if you marry her, until you offer expiation for zhihar.