How is nationalism more significant in the modern era compared to imperialism, socialism, and militarism?
This depends in large part on what you mean by "modern era." In today's world, nationalism is more significant because the other three have largely been discredited and are no longer major factors in world politics.
Imperialism and militarism have been discredited largely because of things like the world wars and advances (we can hope) in overall morality. In past times, there was much more of a feeling that it was appropriate to say that "might makes right." Today, that is an idea that is not well accepted in the world. We have progressed to the point where we realize that wars are terrible things and that taking control of other countries simply because we can is immoral.
Socialism has also largely been discredited. It clearly did not work for the communist countries during the Cold War. China has pretty much given up on socialism and has prospered while countries that have held on, like Cuba and North Korea, have suffered.
That leaves only nationalism, which seems to be a potent and lasting force in world affairs.
Nationalism usually has a militaristic connotation attached to it. Nationalist states are more likely to go to war to protect their idea of what their own nation is. Nationalists want to preserve the traditions and culture of their country. Some nationalists, as in the Middle East, resort to terrorism because of their extreme beliefs. Compared to imperialism, nationalism i less about expanding and developing capital elswhere and is more about the state itself mainting its own identity. Socialsim is a political term that came in the late 19th century and doesn't maintain aspects of militarism like nationalism.