Ok, I have to retract a little. While Jevons and Walras are far more influential, Carl Menger (1840-1921) also apparently made contributions to marginalism. Menger was apparently the founder of the Austrian school. I admit I know little about him. Ditto for the subjective theory of value, which was also created by the above 3 according to wikipedia. Apologies.
Yeah, but, you know…Newton. It’s really no contest, to be honest. 
It is possible to include Coase because he was taught by Hayek and was influenced by him and other Austrians.
If you define the Austrians as Menger, Mises, Hayek, and Rothbard then they were influential but if you define them as people who learned from them and went off on their own then they were the most influential school in the 20th century.
Modern Austrian economics is mostly a fringe as you say (though RBC theories need a second look IMO for smaller countries), but that is because mainstream economics has absorbed so much of Austrian economics. The good ideas of the Austrians have mostly been absorbed and only the extreme stuff is left for the current Austrians. The reason no one reads “The use of knowledge in society” is that it is no longer controversial because no one disputes it. However, as late as the 1987 edition of Samuelson’s textbook was predicting that the Soviet Union would pass the US in gross national income in 2012.
Your cite about Marx says he was right about Business cycles being endemic to industrialized economies, but that he was wrong about the reasons why and the solutions. It claims he was right about the transformative power of the Industrial Revolution, but while he realized how big a change it was he was totally wrong about what kind of change it would be. It also claims he was right about the good things about the Industrial revolution taking longer to manifest than the bad things. I am skeptical of this claim but don’t know enough history to properly judge it.
The things your cite says Marx got wrong, 1.Capital is complementary to labor and not a substitution, 2. Working for wages and not out of public spiritedness is a good thing. 3. Capitalism is capable of producing a distribution of income that leads to prosperity for most people. The three wrong things are pillars of his thought and the three “good” things are minor at best.
As for sociology Marx said that capitalism crated the conditions for inevitable revolution. However there has never been an actual Marxist revolution, they have all been Leninist.
The only lasting thing Marx ever produced was a system of morality based on an oppressor oppressed axis that appeals to a certain type of leftist.
This is fairly ludicrous since if I pay less taxes I will be able to afford the same expenditure by working fewer hours, therefore I would cut down on work as much as possible.
However, I will have to pay more in a free market to private enterprise for the things taxes buy, properly provided by government, such as roads, police, healthcare, water, waste removal, safety regulation, higher education, international influence ( military ) for exports etc. etc.; but I might be able to pay for that by working the same original number of hours — with the unavoidable ‘taxes’ merely going to private enterprise.
No way would lower taxes encourage me to work longer or harder. Life was not meant to be spent working as much as possible: that is a Leninist and libertarian doctrine divorced from reality.
Supply side goes way beyond that.
Mainstream economics says there is an income effect (more disposable income implies more consumption and leisure, i.e. fewer work hours, is a form of consumption. But there’s also a substitution effect: higher wages make working more attractive than leisure, because of, well, the higher payments to working. Which effect outweighs the other is an empirical matter. And empirically the two effects are close to one another. From what I’ve read the substitution effect has an edge.
Supply side stuff goes way beyond that. They say that not only will lower taxes cause people to work more (something that has some mainstream support), but that the extra work will cause total tax receipts to go up.
Simple model. If you want consider “Hours” an agglomeration of time and effort:
Tax receipts = tax rate * Hours worked
Supply siders say that hours will increase more than taxes decrease. Consider a rich guy with a tax rate of 50%. It is proposed that the rate be cut to 40%. For tax receipts to rise, it’s not sufficient for hours to increase. They have to increase by more than 25%. So instead of working a 40 hour week, a tax cut from 50% to 40% causes our executive to work a 51 hour week. There’s no empirical support for such a claim, and when the Laffer Curve was first scribbled on a napkin, none was provided. It’s crackpot stuff.
But supply siders don’t really have any representation in academia. Austrians and Marxists do, but they are fringe. Real business cycle folk are mainstream, though they have little influence in the popular media AFAICT. And there are lots of conservative economists.
Your are going to have to do better than that. Lots of people were taught by lots of people. Samuelson, Arrow and Solow are far more influential than Hayek. Normal people scratch their heads at the claims of Mises. I don’t know a lot about Menger, but I confess I’m pretty dubious about his influence, given that his supposed accomplishments were duplicated by Walras and Jevons.
There were a set of music videos released a few years ago about “Keynes and Hayek”. But that was blatant historical revisionism. There wasn’t any great debate between the 2 men during the 1930s, though they knew each other. Hayek simply didn’t have the stature or frankly the models. If you want to square somebody off against Keynes/Hicks, Milton Friedman would be the guy though he came a little later.
I know little about Rothbard other than his founding of Paleolibertarianism, which is a political movement that drew its explicit inspiration from David Duke and Joe McCarthy.