In 1984, how, according to O'Brien, does the party as an oligarchy differ from Nazism or Russian Communism?
I would add that the key difference between the Party and Nazism/Communism is that the Party explicitly denies that there will come a time when human society is happy, or that this is their aim, even in the distant future. For the Party, torture and repression are what affirms its power.
However unrealistic it may seem to us now, both Nazis and Communists believed and proclaimed that some sort of ultimate happiness and peace for society were their goals (at least, happiness and peace for those worthy to enjoy them, the "master race" or the "proletariat"). In other words, they were non-religious quests for the New Jerusalem. O'Brien flatly and angrily denies that anything like this is the case for the Party:
"Power is in inflicting pain and humiliation....Do you begin to see, then, what kind of world we are creating? It is the exact opposite of the stupid hedonistic Utopias that the old reformers imagined....Progress in our world will be progress towards more pain....If you want a picture of the future, imagine a boot stamping on a human face -- for ever." (Part III, Chapter 3)
In short, the Party can only feel its power if it exercises it against resistance. There must always be dissidents to be tortured and tried, otherwise the Party's rule will become unreal to its members.
This unpleasant picture was inspired partly by Orwell's distaste for the hedonism of many contemporary social reformers such as H. G. Wells.
According to O'Brien, the difference between the Party and Nazism or Russian Communism is that the Party has succeeded in creating no martyrs. The Nazis and Communists tried to do this by exposing their victims to public trials in which their dignity was destroyed, but after a few years the dead men still became martyrs in the memories of the people, and their degradation was forgotten. The Party's system of mind control is so complete, however, that "all confessions...uttered...are true" - the Party makes them true by effectively altering reality. The Party constantly rewrites history and destroys all trace of what really happened by controlling the media and its citizens' minds. Potential martyrs are brainwashed completely in the Ministry of Love, and "lifted clean out from the stream of history" - there will remain absolutely no evidence that they ever even existed (Part 3, Chapter 2).
O'Brien points out another difference between the Party and the German Nazis and Russian Communists in Part 3, Chapter 3 as well. He notes that the Party is unique in that it straightforwardly acknowledges that its ultimate objective is to enjoy power for its own sake.