The main way that Orwell illustrates the wealth and power of the Inner Party is through sheer contrast to everyone and everything that is outside of that inner circle. Almost the entire novel is dedicated to describing the awful circumstances that everyone in Winston's society lives in. The Proles live in hovels, jammed together in their poverty and want. Even Winston, a worker for the Party, lives in discomfort, run-down circumstances, and at the whim of constant rationing and shortages. Everything is miserable and run-down--the housing developments, the food, their clothes, and everything about their living conditions. Even their information and access to truth is rationed; they are told only what the Party wants you to hear. Orwell relates this very well by creating a character, Winston, whose very job it is to alter the truth.
Orwell uses great descriptions to relate the poverty and miserable conditions. In one scene, Winston sits in the canteen bemoaning the dreariness of it all:
He meditated resentfully on the physical texture of life. Had it always been like this? Had food always tasted like this? He looked around the canteen. A low-ceilinged, crowded room, its walls grimy from the contact of innumerable bodies; battered metal tables and chairs...bent spoons, dented trays, course white mugs; all surfaces greasy, grime in every crack...always in your stomach and skin there was a sort of protest, a feeling that you had been cheated of something that you had a right to.
Using that kind of imagery, Orwell paints a scene of misery that contrasts with the luxury that we find in O'Brien's office, which is the only real contact we have with the Inner Circle in the book. There is soft, luxurious, colored carpet. There are soft lights, rich and polished wood; there is real wine and real food, and cigarettes that are in a silver case. Everything speaks of luxury, power and ease. Even more significant: O'Brien can turn the telescreen off. He has the power, the choice to do such a thing. So not only do the Inner Party have access to all of the "rationed" items in life, and live in nice, kept-up, luxurious homes, they can also be free from the draining constraints of always being watched. They have freedom and a wealthy lifestyle.
Orwell uses the contrast between the life of the everyday citizen to the life of an Inner Party member to demonstrate that all of the power was within a very small and privileged group that was the Inner Circle. I hope that those thoughts helped; good luck!