How did the Jews get their revenge when the Holocaust ended?

Judaism, and Jews by and large, are not vengeful. Plain and simple.

Even in prayers that call for revenge, there is never a plea that God, let's say, should protect us and strengthen us when we go out to take revenge, for ourselves, or for Him, or in His name etc. This may be too subtle for some, but there is never any such call in Judaism.

What you DO find on the subject in Jewish prayer is: "Why should the nations say [of Israel] 'Where is their God?' ", and the plea that God Himself work the revenge where it is just and proper.

On the subject of the Holocaust, it's frankly somewhat juvenile to be talking about revenge. Probably no better moment could exist in which to quote Mario Cuomo, the ex-governor of New York state, who said ... on the subject of capital punishment ... "Yes, there's no question that they are animals. But by the grace of God, we are not."

-- The Nazis, who had all of the power, were disgraced, defeated, and no longer exist.

-- Those who had no power, and who the Nazis created a nationwide industry devoted to their utter extermination, still exist, have almost restored their numbers to pre-extermination levels, and have powers of self-determination that have not been seen in 2,000 years.