What literary device does Wiesel use to illustrate his disillusionment with God?

While they could also be considered literary devices, Wiesel adopts common rhetorical devices to express his disillusionment with God, including anaphora and hypophora. Rhetoric is the art of persuasion, and in his book Night, Wiesel very much wants to convince the reader that God not only abandoned the Jews during the Holocaust but singled them out as a group to be persecuted.

In section three at Birkenau, just after the selection, Elie witnesses children...

While they could also be considered literary devices, Wiesel adopts common rhetorical devices to express his disillusionment with God, including anaphora and hypophora. Rhetoric is the art of persuasion, and in his book Night, Wiesel very much wants to convince the reader that God not only abandoned the Jews during the Holocaust but singled them out as a group to be persecuted.

In section three at Birkenau, just after the selection, Elie witnesses children being thrown into a pit of flames. This atrocity seems to be the spark of his retreat from God. He uses the rhetorical device of anaphora in his memory of that first night in a death camp. Anaphora is the repetition of the same word or words at the beginning of successive phrases or sentences:

Never shall I forget that nocturnal silence which deprived me, for all eternity, of the desire to live. Never shall I forget those moments which murdered my God and my soul and turned my dreams to dust. Never shall I forget these things, even if I am condemned to live as long as God himself. Never.

The repetition of the word "Never" has a chilling effect. The senseless killing and torture are something he can never forget. Moreover, he can never forgive God for allowing it. 

In section five the Jews gather together during Rosh Hashanah for prayer. Elie questions why God should be blessed and again uses anaphora in his condemnation, this time repeating the word "Because":

Why, but why should I bless Him? In every fiber I rebelled. Because He had had thousands of children burned in His pits? Because He kept six crematories working night and day, on Sundays and feast days? Because in His great might he had created Auschwitz, Birkenau, Buna, and so many factories of death? 

In section four, Wiesel uses the rhetorical element of hypophora in his expression of disillusionment with God. Hypophora consists of raising a question and then providing an immediate answer. The Jews at Buna witness the hanging of a young boy. The boy doesn't die right away and lingers between life and death for some time while each of the prisoners is made to look into his face. A man near Elie asks a question about God, to which Elie has a quick response:

Behind me, I heard a man asking:

"Where is God now?"

And I heard a voice within me answer him:

“Where is He? Here He is—He is hanging here on this gallows….”