To get back to the original post on what would happen with a southern strategy, this is what I see as being most likely.
1) The Germans achieve great success in early summer as IOTL. Units advance into the Baltics and towards Smolensk. The Soviet counterattack there is contained as IOTL, and seems to give validation to Hitler's southern strategy.
2) If Finland enters the war, the Finns might accept Stalin's offer to return the territories he takes. Since Leningrad and Murmansk are not a priority for Hitler, he may not object to a separate peace so soon. Or precisely because the north is not important, the Finns don't enter the war in 1941.
3) Germans achieve great initial success in the south. Although Sevastapol holds, Germans continue to advance to the Donetsk basin. Their goal is Rostov, Voronezh, and perhaps Stalingrad. Resistance is heavier than expected. The lack of good infrastructure is hurting the Germans. They find out that they do not have enough tanks to replace those that they have lost,a nd the Luftwaffe likewise finds it harder to keep an air umbrella over the advancing troops.
4) Autumn rains halt the advance shortly after German units cross the Donets. Hitler believes the Red Army is out of reserves. Once the ground freezes hard enough for the panzers to roll, Hitler orders an all out attack towards Stalingrad to occupy the Volga and cut off the Caucasus. German troops are increasingly affected by the cold.
5) The Germans overextend their lines, thinking the Red Army has no reserves. A massive Soviet counterattack near Stalingrad forces the unprepared Germans to retreat, causing them to take many casaulties. Hitler orders the army to stand and fight. The southern front lines stabilize somewhere between the Donets and Don.
6) Hitler declares war on the United States after the Japanese bomb Pearl Harbor and invade the Allies' colonies in Southeast Asia.
7) After the initial success of the Stalingrad counter-offensive, Stalin orders attacks in the Baltics and Smolensk. Both are beaten back by prepared German defenses at high cost to the Soviet Union.
8) Hitler plans a new offensive for 1942. He has achieved many of his initial war aims, but the Soviet Union has not collapsed. He thinks their reserves are low, and that another offensive will allow him to gain the Caucasus oil. The German Army makes new preparations.
9) The Red Army now guesses that Hitler's objectives are the economic resources in the South. They plan to deal with an attack there. Note this is different than OTL when the Red Army guessed wrong that Moscow would be the objective.
10) A new German offensive happens in the south. There are additional Italian, Hungarian, and Romanian units. German forces may be slightly larger than IOTL. After some initial success, the Germans run into fierce resistance. They reach the Volga again, but are unable to take Stalingrad. Some German units reach Astrakhan. Others slowly advance into the Caucasus mountains, attempting to reach Baku.
11) If hard pressed to defend the Caucasus, Stalin agrees that several British divisions from the Middle East can enter the Soviet Union. The Germans manage to seize some oil wells north of the mountains, but they find it hard to cross. The line stabilizes with the Germans not reaching Baku.
12) Stavka plans for its next winter offensive. They know that the Germans are overstretched. They decide that they will not attack the Germans at the front near Stalingrad, but well to the west. Their objective is to drive south towards Rostov and cut off the German troops in the Kuban. They mass their armies in secret, and achieve surprise. The rail center at Kurks is retaken. The Red Army crosses the Don and reach the Donets before Germans recover their lines. A salient is formed between the Don and Donets that threatens all German troops to the south.
13) Diversionary attacks by the Soviets elsewhere achieve little success.
14) Determine to enter the war and fight Germans as soon as possible, American troops land in French North Africa in the fall of 1942. Their objective is to seize the entire coast and trap and destroy German and Italian forces between them and the British 8th Army. If this can be done, they plan to invade France in 1943. The plan proves too ambitious as the failure to secure Tunisia allows Hitler to send troops into Tunisia, prolonging the fighting. Eventually, the Germans and Italians surrender.
15) 1943 begins. The German Army has not taken as many casualties as they had IOTL, but the strategic situation is not that different. One major benefit is that the armies of the Axis satellites are not as badly mauled in this timeline. It appears unlikely that Axis forces will be able to seize Baku, and Don salient threatens to possibly cut off all forces to the south. At this time, Hitler considers a separate peace deal with the Russians, if Stalin will agree to the Ukraine being ceded to the Germans. Stalin balks at such a concession. Hitler plans one last summer blitzkrieg to inflict massive casaulties to force Stalin to come to terms.
16) Hitler decides to focus on the salient between the Donets and Don. It has prime economic importance and offers the chance to cut off large numbers of troops. The attack will be vital as failure will mean the troops in the Kuban and Caucasus are at a risk. After a long delay, the attack begins in July 1943.
17) The Soviets have fortified the salient extensively. Despite initial German successes, they are unable to close the gap. Instead, the Russians launch a counterattack. Instead of heading south to Rostoc, they veer west towards the lower Dnieper and Sea of Azov. Another attack strikes Smolensk which is also successful.
18) The long front of the Germans cannot be maintained. Despite the oil wells at Maikop, there are too many troops there being idle. The troops begin evacuation. Some head towards Rostov to keep the route open, but the southernmost units cross into the Crimea. While the Germans have stabilized their lines, they have lost all their 1942 conquests, and are in a worse position than how 1941 ended. However, they are doing slightly better then OTL in terms of casulaties and lost units.
19) The Western Allies invade Sicily and then Italy. In Tehran in late 1943, they promise Stalin that they will invade France in May or June 1944.
20) Hitler decides that the German Army must be on the defensive in the east in 1944 in order to prepare for the inevitable invasion of France.
21) Stalin orders an offensive in the winter of 1944. The Red Army takes Kiev and crosses the Dnieper. They drive south, liberating most of the Ukraine and cutting off German forces in the Crimea.
22) Allies invade Normandy in June 1944. Coordinating their attacks, the Red Army unleashes a new offensive towards Minsk, inflicting heavy German casaulties. Hitler orders his forces in the Baltics to stay so that the Baltic Sea can continue to be used for U-Boat training.
23) After some initial delays, the Western Allies liberate France and drive to the Rhine.
24) Romania, Hungary, and Bulgaria begin secret talks with the Allies to switch sides. Western Allies refuse unless the Soviet Union agrees. Eventually it is agreed that in the spring of 1945 that they can switch sides, but must accept Red Army troops to cross their country so they can aid Tito in Yugoslavia, and cut off German forces in Greece. Britain plans to land troops in Greece to support them.
25) Hoping to push the Western Allies back and obtain a separate peace, Hitler orders a winter offensive in the Ardennes with the objective of the port of Antwerp. It fails, destroying most of the German reserves.
26) In early spring 1945, the Western Allies cross the Rhine and drive towards the Elbe. In the east, the Red Army enters Romania, Hungary, and Bulgaria as those countries change sides. An offensive in the center drives towards Poland.
27) The Western Allied offensive near Berlin stalls as the city's defenses are too great. Rather than waste troops on a prestige target, Eisenhower authroizes Patton to take Prague and attempt to reach Cracow. Other American armies are sent south and reach Vienna, as Allied forces in Italy meet them. Tito's partisans liberate Yugoslavia. American and Red Army troops meet on the Danube near Vienna.
28) As the Red Army nears Warsaw in May 1945, the Polish government in exile launches an uprising supported by American and British airpower. Polish airborne troops are dropped into the city. The Red Army enters most of Poland, but Patton does reach some of prewar Poland, and also occupies some of Silesian territory which is due to be given to the Poles.
29) The Allies agree that Berlin is to be taken by a combined offensive by the Soviets, Americans and British. The Red Army continues through Poland,a nd after heavy fighting crosses the Oder. The British liberate Denmark, opening up the Baltic. The Polish government in exile requests all Polish units be sent to northern Poland so that can have a token presence in the Battle of Berlin. The Americans welcome home to Prague the return of the Czechoslovakian government-in-exile.
30) The Battle of Berlin begins in August 1945. The Americans discuss whether to drop the atomic bomb on Berlin, but decide against it as they need a government to negotiate final surrender. The city surrenders shortly after Hitler kills himself. Karl Donitz, new leader of Germany, surrenders to the combined Allied powers.
31) Occupation zones are similar to that IOTL, but the Western Allies have a northern land bridge to their sectors in Berlin. Americans evacuate Czechoslovakia, and the Red Army established their supply line through that country as the Polish government is insistent that the Red Army cannot stay in Poland. Crisis is averted.
32) In Eastern Europe, Communist regimes establish themselves in Romania, Hungary, Bulgaria, and Yugoslavia. Baltic countries remain part of the Soviet Union. Czechoslovakia retains its democratic government for the time being, but is quite friendly with Moscow. The Poles continue to cause trouble as relations with the Soviet Union deteriorate.
33) Japan surrenders in our time line, but because of the longer war in Europe, the Red Army never enters Manchuria. Nationalist China is able to hold onto Manchuria's industrial assets, and the Red Army does not leave stores of weapons for Mao's Communists to use. This greatly hurts the ability of the Chinese Communists in their upcoming struggle against the Nationalists.