If I marry my ex-wife whom I divorced twice – an irrevocable divorce and then a second one – will it be a new marriage, or will one of the divorces remain counted? And can I atone for my oath not to take her back – where I swore by Allah upon the Noble Qur’an that I would never take her back, and said, "O Lord, if I take this woman back, then deprive me of the scent of Paradise"?

If you divorced your wife less than three times and married her again with a new contract without her marrying someone else, she returns to you, and the remaining divorces are counted against her. If she married another man after your divorce and the expiry of her 'iddah (definition), and then you married her again, scholars have differed, but the majority opinion is that she returns to you, and the remaining divorces are counted against her.

If you swore by Allah or by the Quran not to take her back, you must offer an expiation for an oath (kaffarat yamin (definition)) if you do take her back. As for your statement, "If I take this woman back into my marital bond, then deprive me of the scent of Paradise," this does not fall under the ruling of an oath, and no expiation is required for it. You must repent from uttering such a statement.