There are four divisions within the party, the Ministry of Truth, the Ministry of Love, The Ministry of Plenty, and the Ministry of Peace. All three of these divisions are ironically named, and control aspects of the government and society that are pretty much the opposite of what their names indicate. The Ministry of Truth, for example, where Winston works, deals in re-creating history and altering the past in order to make it fit more perfectly with the Party's ideals and goals at the present moment. They deal in creating lies that support and boost the party. They take truth and destroy it, recreating and tweaking it to fit what the Party needs it to be in order to stay in power. So, it does not minister truth at all, but well-constructed and crafty lies that serve its master, the Party.
The Ministry of Love, which, at the beginning of the novel Winston doesn't know much about, deals in torture and imprisonment. People who rebel against the party are taken there and tortured physically and mentally until they submit to the Party's creeds. They do not minister love, but rather brutal torture and cruelty, all aimed at getting people "love" the party. It is a terrifying place, "the really frightening one," as Winston puts it at the beginning of the novel.
The Ministry of Peace "concerned itself with war." It worked constantly to keep Oceania at war with other nations. It prompted war, dealt in war, controlled the war, and made sure that war fever was at its most impassioned among the people. Peace was its supposed mission, but it attained it through constant warfare. The Ministry of Plenty worked to keep rations coming, which kept the people in a constant state of want. It controlled how much of everything that people were allowed to use. It did not minister plenty, but scarcity.
The ironic naming of these branches are just another propoganda tactic of the Party, an element of newsspeak that phrased awful things in euphemistic phrases, hoping to fool the people and appease them. I hope that helped; good luck!
I am not completely sure I get this question. To me, the functioning of the various parts of the Party doesn't seem all that mysterious.
I imagine that the Inner Party makes all the important decisions. Now, I am not sure what kinds of important decisions really exist in this society. I suppose they decide who to go to war with. And they must decide what things are going to be made in the factories and how the Party is going to keep itself in power. So these people are the brains.
The Outer Party, like Winston, is just the machinery that does what the Inner Party wants. They make the dictionaries and falsify the history in the ways that the Inner Party tells them to.
I do not really see where there is any problem with them working together -- the Party seems to have all its parts pretty well under control.
If that doesn't help, maybe you can respond with your own thoughts...