Inside the Nazi concentration camps, the primary language spoken language was German. German was the main language spoken by all SS officers and guards in all concentration camps in Germany and the death camps in Poland. In other concentration camps and transport camps, like Vught and Westerbork, in the Netherlands, Drancy in France, and Fossoli in Italy, the native languages of those countires were used, alongside German. During the first years of the concentrations camps existance, pre-1940, nearly all prisoners were German. When people from other countries were arrested, the language barrier first began to arise.

Many Jews, especially those from Poland and eastern Europe were also able to speak Yiddish. Yiddish and German both descended from an older form of German and the two language share a lot of similar words, structure, and grammar. Due to that similarity, the Jews who could not speak German, but knew Yiddish, were able to understand the German commands without much issue. Even if some struggled to understand, there was at least others in the same group who translated for the rest.

There were also prisoners assigned to be interpreters. One example is from Livia Bitton-Jackson's memoir. When she arrived in Auschwitz in May 1944, she arrived with a group of Jews from Slovakia and Hungary. She was from Slovakia, but Hungary took over the area years prior, so the group primary spoke Slovak and Hungarian. Some also spoke German, like Livia herself, a language she learned in school prior to being deported. Those who could speak German were ordered to step forward and translate for the group.

Then there is the case for Primo Levi, an Italian Jew who ended up in Auschwitz. He was a Chemist, and much of the material he studied was in German, so he had a slight understanding of the language. He recounted that many of the Italians who were with him died after a short time since they could not understand. He believed that language was a cause of death for many. The Jews who arrived from Greece faced a similar issue. Their languages, Greek and Ladino, were very different from German, and very few among them, knew any German. They were also isolated from other prisoners since they could not understand them either, hence why so few of them survived.

The Jews that arrived from Norway, Denmark (very few), the Netherlands, Luxembourg, and Dutch speak part of Belgium, often understood due to the languages all being from the same language family. Many may have also learned German at some point or spoke Yiddish. In France, many Jews also spoke Yiddish, but many French also learned German at some point in their lives, normally in school, too. Even so, interpreters were also used in most cases to get commands across. The interpretors were responsible from translating German into the language the group of arrivals spoke.

Sources:

Bitton-Jackson, Livia. (1999). I Have Lived a Thousand Years.

Buller, Robin. 2016. The Power of Language: Communication, Memory, and Greek Jews During the Holocaust.

Levi, Primo. (1996). Survival in Auschwitz.