What language did the Holocaust victims speak with each other in the various camps?

By far the most common language spoken by Jews in much of Eastern Europe was Yiddish, There were about 13 million Yiddish speakers worldwide in the late 1940s, about 75% of whom were murdered during the Holocaust. There are likely fewer than 1 million native Yiddish speakers today, though there are a larger number of part-time or non-native speakers. Yiddish was particularly commonly spoken among the Eastern European Jews who were nearly totally wiped out during the Holocaust. As such, in some camps Yiddish became somewhat of a lingua franca. Yiddish remained somewhat of a lingua franca in the post-war displaced persons camps as well before being superseded by English or modern Hebrew. This is particularly true of large camps with a large number of prisoners from different countries, such as Auschwitz. Many survivors recall the Sephardic, non-Yiddish speaking Jews from Greece being particularly targeted in Auschwitz because they could not understand the Nazi's orders. Yiddish draws a great deal from Medieval German, and is therefore partially mutually intelligible with German which allowed many Jews, particularly Eastern European Jews who might not speak German. However, many Jews didn't speak just Yiddish, many also understood the local language of their home country and in Western and Southern Europe many Jews didn't speak Yiddish at all. The six main death camps, all in Poland, in the very heartland of Yiddish. Concentration, labor, and even death camps also developed a kind of "camp talk", with words such as "kapo" for the prisoner overseers of work groups and barracks, or "muselman" the Yiddish word for Muslim which was used for the prisoners about to die, which likely came about because of how these prisoners fell to the ground when they no longer had the strength to stand, taking on a position similar to the prostration done during Muslim prayer. Camps such as Auschwitz, and particularly during the last months of the war camps like Bergen-Belsen, Dachau, and Buchenwald had prisoner populations from many different countries, so dozens of languages were spoken, but for Jewish victims of the Holocaust, Yiddish was perhaps the most common mother-tongue.

"This Way to the Gas Ladies and Gentlemen" by Tadeusz Borowski [a non-Jewish Auschwitz survivor]