Fire is extremely destructive, to the point where one fire expert can probably take on five magicians of similar strength in any other element and wipe the floor with them in a straight fight,

Doesn't sound like. Sounds like all your mages are glass cannon; if a Fire and Water mage start arguing, the Fire mage is probably going to be the one to throw the first firestorm...except the Water mage will see it coming seconds in advance and shoot him. Ditto for other types -- whoever shoots first is going to win.

Also, "The White Hand" and "The Black Hand"? Is anyone ever going to name themselves "The Black Hand"? That's pretty clearly a villain name, and no one thinks of themselves as the bad guys. Also, it sounds like the Black Hand are trying to conquer the world for the Evulz; consider coming up with a better motivation. Maybe they have had the prophetic dreams of the nuke destroying the world and they tried to work with the White Hand to prevent it but there was too much friction, so the only option to save the world is for them to control everything. Or maybe the Black Hand was a monarchy / some other form of autocracy / theism / secular nation and the White Hand tried to forcibly impose democracy / atheism / religion on them "in the interest of saving the people"? Or maybe they share a religion and one side has been bogarting the equivalent of Jerusalem, so this is a war of religious freedom? Just because there is a non-evil reason for them to be taking over the world doesn't mean you can't have rational!Mengele in charge (or, at least, as a high officer).

Okay, exploiting the oaths. My understanding is that the oath doesn't give you any extra skills or knowledge, it just requires you to do something to the best of your ability.

1. Criminal recidivism is no longer a thing. If you are convicted, you take an oath to go straight.
2. Political scandals are no longer a thing. When you take office you take an oath to be moral, upstanding, and to serve the nation selflessly.
3. Traitors in the military, also no longer a thing.
4. Traitors in any position of trust, no longer a thing.
5. Corporate scandals, not a thing. CEOs and senior officers take an oath to serve the stockholder's interests second to those of society. You'll need careful phrasing on that one.
6. Every single person in the nation takes an oath to be completely open and honest in court, should they ever end up there. Judges take an oath to be fair and impartial. Lawyers take an oath to not overcharge, and to do at least N hours of pro bono work per year so that poor people can have access to good representation too.
7. Everyone takes an oath to get at least 1 hour of exercise per day and not overeat. Boom, goodbye obesity and much of diabetes. (handwave, thyroid conditions, etc, handwave)
8. Everyone takes an oath to go to the doctor once a year and the dentist twice a year. Boom, massively reduced health care costs.
9. Everyone takes an oath not to murder, steal, rape, become addicted to anything, etc. You'd need an escape clause for military service.
10. If you want to get edgy you could make citizens take an oath of "I shall not discriminate" in order to get rid of racism, sexism, and classism. That's dodgy and failure-prone, though.