With or without hindsight?
With hindsight to improve strategic judgment (it's more fun) but without using "special knowledge" that no one then could have had. (I.e. fixing BAMS because the Germans were reading it. We know that now; Rodger Winn strongly suspected it then; but no one on the Allied side had actionable knowledge then. Or moving
Queen Elizabeth and
Valiant out of Alexandria to evade the 12/19/41 frogman attack.)
There are however strategic decisions which could have been made differently then and in hindsight should have been. So, for Europe:
- Do whatever is necessary to blockade North Africa, and totally cut off Axis supplies. This will be up-front expensive in ships (we'll probably lose several cruisers and a flock of destroyers) but enormously less costly than another year of fighting in North Africa.
- The Battle of the Atlantic is not yet won; the success of late 1941 could collapse if the Germans upgrade the Enigma used by U-boats (which is what happened OTL). Prepare for that possibility.
- Start building lots of escort carriers now. A few were coming out then (Audacity went into service in September 1941; her planes shot down seven Fw 200 Condors and sank a U-boat before she was sunk in December), but mass production was a year away. Start converting any usable ships as fast as possible.
- Allocate all available VLR aircraft to ASW in the Atlantic (that are not employed in the Pacific).
- Large-scale political infiltration campaigns directed at Vichy France, the French colonies including North Africa, and Axis ally states, including Italy. Use persuasion, bribery, even blackmail to promote a faction that wants to get out of the Axis and join the Allied bandwagon. There are lots of opportunists, trimmers, and grafters to be bought with money or future political favors; and also genuine patriots who can be persuaded their nation's interests lie with the Allies. (These sets overlap.) Paying a Vichy general a million dollars under the table and promising him post-war "hero" status is cheaper than fighting even a small campaign. Getting Bulgaria or Romania to flip early would be worth a lot.
- Work for and prepare for possible Italian surrender. (We know now it would happen; it was at least imaginable in 1941.) Thus, when it does happen, be prepared to seize as many Italian-held key points as possible - the Dodecanese, Corfu, ports in Albania - as well as Italy, thereby gaining beachheads in the Balkans without having to do amphibious attacks.
- Contact the Schwarz Kapelle, and collaborate with them on killing Hitler, overthrowing the Nazis, and getting Germany to surrender. The first two they want as much as the Allies do. The Allies can demand surrender without implicitly threatening Morgenthau Plan-type Carthaginian terms, and still insist on German occupation and complete, permanent disarmament. If the SK won't deal - the Allies still bomb Germany into ruins and kill millions of German soldiers. They'll cave a lot earlier than Hitler would. (Note: if Stalin objects, tell him to stuff it where the sun don't shine. He openly supported Hitler for years - he has no standing to complain about anyone else's dealings with other non-Nazi Germans.)
- While we're at at: make further Lend-Lease aid conditional on Stalin's public pledge (published in the Soviet state media) to honor all 1939 boundaries. The Western Allies were fairly soft-headed about the USSR (Harry Hopkins wrote in his diary that Stalin's rule was essential to peace and democracy in Russia), but the evidence was there for realism. In hindsight, this evidence should have been collated and properly analyzed, and appropriate hard-harded policies adopted. Offer joint occupation of Germany and other Axis countries (the occupation forces and officials to be 1/3 British, 1/3 American, 1/3 Soviet).
With these policies and strategies in place - Italy surrenders in early 1943, the Nazis probably fall in mid-1943, the rest of the Axis bails out, and Germany surrenders in late 1943/early 1944.
- Do whatever is possible to prevent the fall of Burma; that may include evacuating troops from Malaya to Burma. This will prevent a major Allied defeat in Burma, but more importantly, it will allow the Allies to supply China far more effectively. See below for the importance of this.
I'll have to finish this later.
OK, continuing...
- Follow OTL's general strategy in the Pacific; there really isn't much to do better without using "special knowledge". Maybe fix the US torpedo problem sooner; it could have been recognized much earlier.
- OK, re China. If the Allies hold Burma, that allows war materiel to reach China without the enormous cost of flying "over the Hump". It also allows heavier equipment to be delivered, included jeeps, trucks, and even light tanks. And a corps or so of American troops; some as "cadre" to stiffen Chinese forces, some as "hammers" to deliver hard strikes against Japanese forces. Lean on Chiang as needed: if the RoC isn't seen as defeating the Japanese, the RoC will lose China - and that is perhaps the most important outcome of the war, though really a post-war consequence.
- Meanwhile, the British, having avoided disaster in Burma and not engaged in North Africa after mid-1942, should have the resources to counter-attack from Burma into Malaya in 1943; and to drive across Thailand to Indochina.
ISTM that Japanese troops were highly effective as light infantry and in die-hard defense of congested terrain (mountains, jungles, islands). But in more conventional warfare, larger scale battles of maneuver, they were very vulnerable. "Heavy" forces (e.g. American/Soviet forces with tanks and a full suite of infantry support weapons) could smash them. That's what would happen in the Asian mainland theaters.
By mid-1944, the US will be in the Marianas (as OTL), but the British and Chinese could be approaching the South China Sea. That exposes the core of the Japanese conquests, and allows the Allies to cut off Japan's oil from the East Indies. The Philippines should fall rapidly, allowing US aid to reach China directly. By the end of 1944, the Chinese should have regained Nanking and Shanghai, and be moving on Peking , while the US takes the Ryukyus and the British clean out the Indies.
The US and Britain tell Stalin to keep his hands off East Asia; if he's a good boy, the USSR will get Karafuto (southern Sakhalin) and the Kurils for nothing.
The war ends a year earlier in Europe; possibly several months earlier in the Pacific. The Bomb won't be ready any sooner; what else might make Japan surrender? Perhaps the threat of invasion with Chinese troops, who will be available. The hard-liners' last fantasy was that on Japanese soil, they could stage
really big banzai attacks and kill enough Americans to shock the US into making peace. That won't work with China.
Bottom line:
In Europe, earlier total defeat of the Axis and probably substantially reduced Nazi murders. The Soviet "bloc" frontier in Europe will be well east of OTL. ("Bloc" in quotes because the USSR will not have satellites.) The Soviets get
presence in more of Europe than OTL (as 1/3 occupiers of all Germany and perhaps Italy), but they don't get
control of the areas they took over OTL, and their meddling will fail IMO.
In Asia, earlier total defeat of Japan, no Soviet occupation of Manchuria and North Korea, and (one hopes) the RoC in position to defeat Communist rebellion after the war. If China is not Communist, the Cold War will be much more favorable to the US side. (Imagine Chinese-American bases in Sinkiang.)
What happens later is not in the remit of the OP.