Operation Russian Freedom
Lets assume the Soviet Union is treated like Germany was after World War II...unconditional surrender, occupation, military disarmed, something like the Marshall Plan is enacted to help them rebuild, and free elections are held in which the communists may or may not be allowed to participate.
OK but the Soviet Union is not Germany. Occupying, deStalinizing and rebuilding the Soviet Union is going to end up being closer to current Iraq than postwar Germany and Japan only an order of magnitude harder. I see a Communist underground resistance plus widespread anarchy. The logical communication centers are going to be unsafe to occupy for a while due to residual radioactivity. To reduce the scope of the problem first the Baltic then the central Asian republics are given independence quickly. Within 24 months the starvation deaths in Russia will approach the war deaths.
To introduce a comic element into this tragedy, I see 3 or 4 'Anastasias' coming forward to claim the Romanov throne.
As for China I'd see the logical US approach would be to send the Nationalist Chinese back in. At best this strategy will partially work. Chiang will end up needing some American boots on the ground to help prop himself up and even then he will control maybe half the country. In addition to Communist diehards there would be warlords. Starvation deaths will be double war deaths within 12 months.
I think Ike is still probable as President but I wonder if he might be tempted to run as a Democrat in TTL. Where I am going out on a limb is predicting that he stands a good chance of being a one term President as the mounting cost and frustrations of a world building program that has clearly bitten off more than it can chew turns Americans sour.
Getting back to the war itself even if the CONUS is untouched by enemy weapons there would be Nuclear Panic among the citizenry as many would think that they would be Abombed any minute. Look for unofficial partial evacuations of the major cities, an increase in suicides, End of Days religious hysteria and other mass dementia.
Germany would suffer a lot during the war. Widespread use of nerve gas would cause massive civilian deaths. Sympathy for German suffering would I think overcome worries about a united Germany so I see a reunited Germany within 3 years with a 50/50 chance that it may include Austria as well.
One thing that could seriously backfire on the US postwar would be if they went ahead and tested an HBomb. I could see all the foreign and not a few domestic newspapers lamenting, "Why oh why does the United States need a bigger bomb?!" This will lend fuel to those who will want to label Uncle Sam the Atomic Bully.
An ancillary to that is delivery systems. When the B-52 comes out the same newspapers will lament, "Why oh why does the United States need a new bomber?" Look for a production run < 100 bombers which will cause Lemay to go ballistic.
Speaking of ballistic the controversy over the B-52 may cause a moratorium on new delivery systems, esp. ICBMs. This will along with no Sputnik will contribute to a much delayed space program. Quite possibly the first satellite is not launched until the early 1970's and then by a consortium of multinational corporations with government subsidies. Hmm a semiprivate space program.
Marxism is not dead in TTL. Outside of sections of Occupied Russia Stalinism is dead but the popular and intellectual appeal of Marx is not going away. Look for essentially Trostskyite Communism to have broad appeal.
An interesting religious delta. Look for Pius XII to write a highly controversial encyclical to passionately defend the justness of WWIII in Thomistic terms, praising Truman several times and Lemay at least one. Look for a hostile reaction within the Church to what will be derided as the St. Curtis encyclical.
I am surprised this WI has not garnered more interest. Where is Calbear when you need him?