What were the words the people used to describe the Nazis?

This is somewhat of a subjective question, the answer would differ depending on exactly who these people in question were. For example German nationals in the 1930s and 1940s would likely have different sentiments towards Nazis than an average American at that time. The term Nazi is originally derived from a German word "Nationalsozialist" meaning National Socialist. These people were supporters of the "Nationalsozialistische Deutsche Arbeiterpartei" or National Socialist German Workers Party. These individuals, now commonly referred to as Nazis, saw themselves as victims of longstanding oppression of the German people. The plight of the Nazis was that the Treaty of Versailles, which ended WWI, had brought the nation to its knees. Nazis saw it as their mission to rebuild Germany to its former glory and assert their dominance as a global power: ideals that are all laid out in Adolf Hitler's "Mein Kamf."
For members of the Nazi party and other supporters in Germany, joining the Nazis was a just undertaking to avenge all of the wrongs imposed upon them. They set out to rebuild their military, address the staggering levels of unemployment, annex territory they felt belonged to them, and hold those responsible accountable. For Germans in the 1930s and 1940s Nazis could be referred to politically as National Socialists. To the layman, they were seen as heroes and visionaries. As the Nazis developed, so did their ideology. They began to take a much darker stance on the plight of the Germans, one that focused on distorted views on race. As campaigns were launched against those they deemed inferior, including Jews and Gypsies, the Nazis began referring to themselves with terms such as "Aryans" or the "Master Race".
On the opposite end of the spectrum, a majority of the free world viewed the Nazis as a dangerous and simply evil organization. As newsreels and pictures began making their way to the allied nations they depicted the massive rallies and marches taking place in Germany. With this the rest of the world began developing their own perception of the Nazis. Many in the United Kingdom and United States, for example, terms like fascist, anti-semites, radicals, and fanatics were used to describe them. In time as the world fell into war, pejorative terms developed as well including Kraut, Hun, and Jerry. All of which referred to the Nazis in a condescending and offensive manner.
Overall there were many terms used to identify and describe the Nazis; all of which are to a degree subjective. At the height of their power the Nazis had a tremendous impact on the world as a whole. Across nations, cultures, political and religious beliefs, people came to know the Nazis in a number of ways. As you research and investigate further into any aspect of that era, you will continue to discover terms, ideas, and ideals that developed as a direct result of a groups individual experiences and exposure to the Nazi party.