Menger used this insight to resolve the diamond-water paradox that had baffled Adam Smith (see marginalism). He also used it to refute the labor theory of value. Goods acquire their value, he showed, not because of the amount of labor used in producing them, but because of their ability to satisfy people’s wants. Indeed, Menger turned the labor theory of value on its head. If the value of goods is determined by the importance of the wants they satisfy, then the value of labor and other inputs of production (he called them “goods of a higher order”) derive from their ability to produce these goods. Mainstream economists still accept this theory, which they call the theory of “derived demand.”

Menger used his “subjective theory of value” to arrive at one of the most powerful insights in economics: both sides gain from exchange. People will exchange something they value less for something they value more. Because both trading partners do this, both gain. This insight led him to see that middlemen are highly productive: they facilitate transactions that benefit those they buy from and those they sell to. Without the middlemen, these transactions either would not have taken place or would have been more costly.

https://www.econlib.org/library/Enc/bios/Menger.html

What happens when there is an oligopoly in the supply of labor?

Same answer. Nothing good for the consumers of labor.

True for both Marxist and neoclassical economics.