Identify the key actors, events, and dynamics that you believe each theoretical lens (Realism, liberalism, radicalism, and constructivism) would highlight for each of the following historical periods: (1) Westphalia(2) nineteenthth-century Europe(3) interwar and WWII(4) Cold War(5) immediate post-Cold War(6) the new millennium

This is an extraordinarily detailed question, and to answer it sufficiently would require the span of several books. However, you can begin to break it down by considering what each of these theories represents and in what time period you believe they would have been predominant.
Realism was both a literary and artistic movement that gained momentum primarily in the middle of the nineteenth century. Realism was a response to the romantic movement of the early century, which authors like Goethe, Fichte, Schelling, Wordsworth, Thoreau, and others used to criticize the growing materialism associated with the European Industrial Revolution. Romantic writing celebrated the beauty and inner-perfection that human beings were capable of achieving and stressed the primacy of natural motifs and their relationship to the human soul.
Realist authors like Daniel Defoe, Ian Watt, and Mark Twain rearticulated the criticisms of the Romantic literary genre to modern industrial society. Instead of focusing on the sublime, realists portrayed life in the cities and countryside as it really was—in an attempt to provide narratives that did not water-down the horrors that industrialization had produced.
Liberalism and liberal thought prospered primarily in the eighteenth century. Its most famous proponents included thinkers such as the American founding fathers (Franklin, Jefferson, Hamilton, etc.) in addition to British and continental philosophers. John Locke was one of the most famous liberal theorists. He wrote Two Treatises of Government which explored the conditions necessary to create liberal democracy and a free society. Locke argued that civil society attains full political and social maturity once governments operate by the will of the people and once their function has been legitimized via the power of the people themselves.
Locke argued that it was the responsibility of civil government above all to protect property and private ownership; in those societies, the people could make decisions freely, and a rationally-organized distribution of wealth would be the result.
One can identify radicalism and radical thought in many different epochs of European history. The French Jacobins were some of the most radical thinkers of the French Revolutionary period, calling for the execution of any and every person associated with the aristocratic classes of the Bourbon monarchy.
The proliferation of socialist thought in the mid- to late-nineteenth century—specifically by theorists such as Charles Fourier in France, Karl Marx and Frederic Engels in Germany, Robert Owen in the United States, and Vladimir Lenin and Leon Trotsky in Russia—led to a period of global revolutionary fervor and nationalist sentimentality, the impacts of which can still be felt in the twenty-first century. Radical revolutionaries of the mid-twentieth century, particularly the famed guerilla leader Che Guevara, inspired a generation of anti-colonial resistance movements in the Third World.
Constructivism was a theory which also gained currency in the nineteenth century; it posits that human societies create knowledge that leads to the proliferation of shared assumptions about reality and civilization. Its contributors are many, and constructivism has led to a rethinking of the fundamental assumptions that have traditionally provided a solid foundation to scientific, sociological, natural, epistemological, and other branches of knowledge. A good (but by no means singular) example of a constructivist is the French sociologist Emile Durkheim.
Durkheim argued that the fundamental presuppositions about reality, religion, nature, and other domains of knowledge only come about through a social understanding of them. In other words, knowledge is something shared between members of a community, and the coordination of individual understandings of a given topic between members of a community leads to the construction of knowledge itself at the larger, social level.
Using these general summaries of each theory (and, of course, your own knowledge), you can make some convincing arguments for what people and ideas were most influential for a given historical period. For example, you might consider the impact of the radical thought of someone like Guevara on influencing Cold War politics both in the Third World and between the US and USSR.
Or, perhaps you might like to consider how the seventeenth-century Peace of Westphalia, which brought an end to the European wars of religion, contributed to the rise of scientific thought, the scientific revolution, and the Industrial Revolution and how, because of this influence, literary and artistic realism were able to emerge in response. The possibilities are truly endless.