WTO Red Storm II and final mission

I'm going to assume you have good generals (Guderian, Badoglio, etc.), nuclear technology lvl2+, missiles lvl1+, and air force lvl3+ for these. All of the tech is pretty cheap even if you don't have them.

tl;dr for the WTO missions: Build lots of nukes, then unleash a nuclear Armageddon on your enemies.

WTO 5
tl;dr: Assign all generals at the beginning, make loads of nukes, and save up to nuke+paratroopers London, Dublin, and the American carrier

As often as possible, make nukes until you have 5 for lower difficulties or 7 for gold. You have enough forces at the beginning to wipe out the French.

If you trust your generals, you can take out de Gaulle normally; otherwise use the nuke you have at the start to weaken him.

Immediately move on to capture Paris. If your generals still have a decent amount of health, you can capture some other French cities as well to boost your economy or gain access to missiles.

Defend against Bradley if he landed, and save up until you have enough resources to capture London, Dublin, and destroy the carrier in one turn in case the British retake the cities. Specifically, nuke London two or three times, capture it with a paratrooper from Paris, nuke Dublin two or three times, capture it with a paratrooper from London, nuke the carrier, and bomb the last 40 health away from him.

WTO 6
tl;dr: Assign all generals at the beginning, make loads of nukes (again), capture and defend the nuclear facility and level 3 airport near Denver, and nuke the last three objectives

Like in WTO 5, constantly build nukes. The forces you have should be enough.

Quickly capture San Francisco, move on to Los Angeles, and defeat Clark and Macarthur, with or without nukes. Push forward to Denver and feel free to nuke it.

From Denver, capture the nuclear facility to its north and the airport to the northeast for paratroopers.

Defending against Devers, Bradley, and even possibly Simonds is the most important phase so you don't have to retake the cities you fought so hard to capture. While that happens, keep building nukes until you have 6 or 9 stored up depending on the difficulty. Nuke Washington, Ottawa, and New York, and have your paratroopers fly in for the final victory.

NATO 6
I don't have a good strategy for this one, so can't help you much here