Boy, I missed this thread, and me a military historian…
The simple answer to the question posted is yes, absolutely. The Axis would have easily won the war w/o U.S. involvement. The question is what form would that victory have taken, and how long until WWIII would have followed. I am also going to assume that U.S support of the Allies would have been limited to selling them what they could pay for. ( I realize real world realities such as FDR make this uncertain, but the OP said “neutral”, so neutral we shall assume) A couple of misconceptions here. Would Germany have occupied all of Russia? Not a snowballs chance in hell. I do believe, as other posters have mentioned, that without the drain on resourses required to counter the Anglo-American threat, that Germany could have forced Russia to sue for peace, stabelizing the lines along the Leningrad, Moscow, Stalingrad front. It would also have given Germany access to one critical thing, also previously mentioned-oil) Stalin would have used the time, of course, to build up his forces to retake the land occupied, but that is not the subject here.
In the west, just as Germany had no chance of occupying Britan, England had no chance of doing anything in Europe proper w/o American support. We would have “Fortreess Britain” right across the channel from “Fortress Europe” and the war would have cooled down a bit. Hitler might very well have occupied Spain, and doing so would make Britian’s continued domination of the Med problamatic at best. ( again, remember, if resourses are not going to be used for one purpose( maintaining a strong defense against probable Anglo-American attacks), they can be used for another( Stabelizing the Eastern front on the Leningrad/Moscow/Stalingrad line, or taking Spain, for example(and a Germany victorious in Russia might likely have found a Spain quite willing to acomodate her wishes))) The Nazis could then have conceded North Africa ( for the moment), consolidated what they held, and planned for the future. It would have become, to coin a phrase, a “cold” war.
In the Pacific, without U.S. involvement, Japan would certainly have held sway. They would occupy Korea and the area of China on a line from Manchuria dowm through Rangoon in Burma. They would easialy have occupied Sumatra, Java, the Celebes and New Guinea, giving them access to their coveted “Southern Resourse Area”. As a practical matter they would need to occupy the Philippine, Marshall, Caroline, and Marianas islands, and how they could do that without fighting the U.S. I have NO idea, but if ( as per the OP, we assume that U.S. neutrality is a given, it would have been easy.( a TOTALLY isolationist U.S. Congress, maybe?) At this point they would have stoped as well, most likely. ( Remember, Japan did most of this even while fighting the U.S. Their navy was the most powerful in the world at the time. Yorktown, assisted by other U.S Navy forces sank or severly dammaged Six major carriers at Coral Sea and Midway, without that, the Japanese Navy is still the 800lb gorilla of the Pacific Ocean. I foresee this as the end of WWII. Unfortunately, WWIII would shortly follow as either A: Stalin counterattacks to take back the areas of Russia occupied by Germany, B: Germany and Japan attempt to link up by driving into the Middle East and India respectively, or more likely, both.