What is the legitimate way out for a person who broke an oath in which he said: "I swear by Allah for His granting me success, health, and a future," and "I swear by Allah an oath for which there is absolutely no expiation, and Allah knows what I say and comprehends it"?

Supplicating against oneself is forbidden and is not a means of compelling oneself to abstain from prohibitions. It is hoped that such a supplication will not be answered, as it falls under idle talk for which there is no accountability. If you supplicate to Allah to protect you from the evil of what you supplicated against yourself, that is good. No expiation is required of you other than what you have already given, unless you repeatedly break the oath and intended the repetition.