How much were they really producing? Can anyone give me some statistics on how much value they made and exported? Were they really the industrial giant that outproduced the rest of the world?
To focus on just a portion of your question, Martin Van Creveld has some interesting things to say about wartime aircraft production. Beyond the pure numbers, he examines production as a function of industrial potential.
Taking the period 1940-45 as the best available compromise, we find that, in those six years, the United States produced 309,761 aircraft. Germany built 109,586, the British Empire 143,234, the Soviet Union 147,836, and Japan 74,646. Earlier in this chapter it was estimated that, if America's industrial potential in 1939 stood at 3, then the figures for Germany, the British Empire, the Soviet Union, and Japan were 1.2, 1, 0.8, and 0.5 respectively. Combining the two sets we find that Germany produced somewhat less than its fair share of aircraft. The British Empire produced considerably more, and the USSR many more. Japan, too, produced more than its share. This calculation ignores many factors, including the extent to which the various countries mobilized their resources and the types of aircraft each produced. Still we conclude that, relative to their overall industrial potential, all the main belligerents except Germany built more aircraft than the United States did. (emphasis in original)
The author does point out that the US made far more four engine planes than any of the other combatants, and these were incredibly more costly and complex than a single engine scout/courier plane. So, in pure numbers, the above numbers show that the US dwarfed all other belligerents in terms of aircraft production. Given that the US also produced more four engined heavy bombers than the other nations involved, including the incredibly complex B-29, we can see that US wartime production was nothing short of lavish. However, even those incredible numbers show that the US didn't maximize its production in terms of aircraft. One can interpret this in a number of ways, but the fact that the US underproduced relative to industrial potential yet still outproduced all of the other nations by a wide margin can be seen as reflective of the genuinely massive industrial power of the country. To put it simply, the US dominated aircraft production in WWII and it wasn't even operating at its potential peak.
I hope that answers your question at least in part. As always, followup questions from OP and others are always encouraged!
To fully answer this question, you should check out Maury Klein's new book "A Call to Arms: Mobilizing America for World War II". This 775 page book was published in 2013 and has 74 pages of end notes. It takes a close look at the home front during WWII and how government, industry and labor overcame their differences and material shortages to become the Arsenal of Democracy. It looks at the hard facts, not the myths.