Are the neoclassical rules, for literature, still relevant today? Or are they still influencing they way we write novels, theatre, etc.?
The neoclassical age roughly spanned the late 17th century through the early 19th century. Although neoclassicism refers to a specific time in history, it also refers to a set of characteristics and motivations for art. So, while you can't claim a modern text to be historically neoclassical, you can show how a modern text is influenced by, or resembles in theme/style, neoclassical texts.
The neoclassical era was formed by artists who valued the classical works of Ancient Greece and Rome. The neoclassical era also coincided with the Age of Enlightenment. So, the era was characterized by an homage to the ancients as well as a growing interest in reason, science and intellectualism. Consequently, writers were as interested in politics and intellectual precision as much as they were interested in imaginative or mythological narratives. Swift's Gulliver's Travels is an adventure, similar to an epic like The Odyssey. But it is also a political satire of British politics. So, here we have an homage to the ancients as well as a (then) contemporary commentary on an intellectual/social issue.
Neoclassical works were often didactic, which is to say there was a lesson or moral point to be made. For example, Alexander Pope's The Rape of the Lockis a mock epic, a satire pointing out the trivialities of the aristocracy.
Consider this progression: The Odyssey, Robinson Crusoe, Castaway. All of these works are epics in the sense that there is a hero/traveler that must endure hardships and eventually return with a new understanding about life. In the latter two (Crusoe and Chuck Noland in Castaway), both men learn to live outside of the industrialized world and they learn the value of time. In this sense, both texts are an homage to ancient epics and they both make some (didactic) commentary on a social issue (the pros and cons of industrialization).
It might be easier to find contemporary works that illustrate influence from the later periods such as Romanticism, Modernism, and Postmodernism. But there certainly are Neoclassical-esque works today. Another modern work that showcases a hero, a journey, an intellectual point, and an homage to the mythical epic is Life of Pi. Pi, the protagonist/hero, stranded like Crusoe and Noland, learns how to survive and continues to learn how to embrace his seemingly contradictory love for both science and religion. Pi is morally and scientifically strict but he is also quite imaginative so this is a work which shows Neoclassical and Romantic influences.