In one notable case, I decided to encircle a stack in Manchuria by nuking the two provinces flanking it and immediately moving in. That proved hard due to low infrastructure and mountain terrain. More stacks surrounded me and I had to drop two more nukes to clear them. Then the province was encircled and I gradually retreated off the peninsula. South Manchuria was left an irradiated wasteland, about 2 million Comintern troops were killed or taken prisoner and some 200,000 Americans and an unknown but high number of Allied troops perished.
In Europe I raided northern France and Germany, even reaching as far away as Austria (coming from Denmark) before Soviet reinforcements arrived.
I wiped out quite a few moving/retreating Soviet divisions just by aerial bombardment.
South Africa, though part of the continent, was an extremity I could afford to hold for a time. Starting from 1946 I reinforced it and pushed all the way to the Congo's borders, using the space between Angola and Mozambique (Portugal was neutral) as a chokepoint. Then once enemy reinforcements piled up I had to evacuate, leaving a handful of South African divisions to fight out their last stand and die without any aid.
I prioritized research into Air Cavalry out of curiosity. I was pleased with the result -small divisions with just 5,000 men but impressive 50 Speed, a powerful tool for encirclements. The best part with playing past 1945 is seeing all those high-tech toys.

I didn't take military control of India and sent no reinforcements, expecting just to retreat to Ceylon after a brief resistance. The Raj AI surprised me by holding out for a year on the shores of the Indus. With Ceylon safe the British Indian Army was evacuated intact and redeployed to the extremity of Burma near Indochina. There, in the mountains with fortresses beneath a river they held up. The Soviets built up immense stacks with over 150 divisions but didn't attack.
This is where the decisive battle was fought. I bought an Indochinese province, built an airstrip, brought in huge air fleets, my 12 airborne divisions and some mobile forces to reinforce the Indians. The remainder of my Okinawan forces, veterans of the Korean campaigns, were prepared for a landing in Rangoon. Simultaneously with this landing, I dropped my paratroopers right behind the stacks, which were then neutralized with two nukes. Stalin lost at least a fourth of his army strength.
I left a defense in eastern Burma and moved excess forces back to Okinawa (where they attacked Korea yet again) and the paratroopers to Europe. There, in 1952, with the Comintern weakened, I launched the final battle. While Marines from the Canaries landed in Cádiz, forces stationed in Britain attacked Bordeaux and followed down the first French river line after the Pyrenees (the Garonne), cutting off Soviet garrisons in Spain. Those were encircled and, with free Gibraltar, I cleared the Mediterranean islands.
And now came the last strike -landings in Marseille and Antwerpen followed by a drive through the Rhine and Rhone, cutting off all Soviet forces in France. After they were encircled, the USSR only had skeleton forces in all fronts. I had all but won the war and got bored again.