The first thing is to realize that Deleuze and Guattari in Anti-Oedipus are trying to break out of the mold of individualism that dominates our culture. That is not the only thing but that is a big part of what they are doing.
So the develop levels below and above the individual organism to focus upon. One level above is the socius. And another level below is the “desiring machines” This is a very unfortunate choice of terms. They mean what Melanie Kline calls partial objects. They mean something like what Foucault calls “practices”. The word “machine” is suppose to be prior to the difference between subject and object arising. It is meant to indicate something that is involuntary within us. Desiring Machines are meant to be organized in Rhizomes. A Rhizome is a heterarchical network. These desiring machines are meant to be organized across bodies. That means the individual body is not a boundary that they necessarily respect. But they exist in a wider field called the socius. So the real level of analysis that they are suggesting is the desiring machines within a heterarchical network embedded in the socius, which may run counter to the way we might cut up things in terms of bodily individuals.
As a sociologist I like this theory a lot. And I especially like the way that its layers correspond to what I call the Special Systems in my theory called Reflexive Autopoietic Dissipative Special Systems Theory. See http://works.bepress.com/kent_palmer
There is of course a lot of things missing in this theory. One thing is the fact that human beings in their practices do more than merely desire. So I have added the opposite of desire which is avoidance. And I have added a separate opposition which is dissemination and absorption. I call these dissipative ordering practices after Prigogine. I think if you make this modification in their theory then it has more explanatory value and is less nihilistic.
There is an interesting metaphor they use for the desiring machines which is a general with his medals hanging off of his chest. Each desiring machine is in some sense a surplus, but perhaps also a lack. The body is decorated with them. They point to the savage stage where there is tattooing as a concrete trace of the desiring machines with respect to the body.
The body without organs is a virtual body made up of these desiring machines which haunts the real body. The real body of the individual has organs, like the body without organs has desiring machines or dissipative ordering practices. In primitive society tattooing was meant to mark the individual so that they could not be kidnapped by another tribe, so that they were always part of the body of the tribe. Thus the tattoo was an inscription of the socius on the individual’s body producing the virtual body which is made up of desiring machines.
Anyway that is my understanding of the background theory. What is your understanding?