Reading these books leaves me dumbstruck
Unsurprising. It was my first reaction; and one D+G pick up from Nietzsche; they're using the aesthetics of the transgressive; which in certain fields - ie Art has been reduced to banality; but philosophy with its dedication to Enlightment Reason is virgin soil for such virile techniques.
Delueze & Guatarri take language hostage; they use language in a way that is not normally used; thus they require interpretation and commentary; one can then decide whether one can agree with their ideas or not.
Gayatri Spivak, post-colonialist critic in her well-known paper Can the Subaltern Speak describes Anti-Oedipus as a brilliantly poetic and radical work - whilst criticising it for preserving the Subject of the West; her own commitment coming from the Marxist tradition is to the marginalised - the subaltern, a term deployed by Gramsci to expand (and globalise) Marxs notion of the proletariat.
The use of language by D+G suggests to me the Symbolist movement in literature - which reacted against the realist and naturalist style; one might point out a parallel here to the analytic school (tending towards naturalism, socratic & logical) and the continental as towards the imaginative, pre-socratic and the poetic.
There are a couple of articles on wikipedia that are usefully explanatory:
Body with organs often abbreviated as BwO. This is lifted from a poem by Antonin Artuad To have done with the judgement of God:
When you will have made him a body without organs,
then you will have delivered him from all his automatic reactions
and restored him to his true freedom
The title of the poem reveals Deleuzes fascination with the thought of Nietzsche (he was one of the few to revive Nietzsches reputation from the suspicion of fascism) and the surrealists fascination of the affects and intensities of the body.
"The Earth," they write, "is a body without organs. This body without organs is permeated by unformed, unstable matters, by flows in all directions, by free intensities or nomadic singularities, by mad or transitory particles" (A Thousand Plateaus, p. 40).
That is, we usually think of the world as composed of relatively stable entities ("bodies," beings). But these bodies are really composed of sets of flows moving at various speeds (rocks and mountains as very slow-moving flows; living things as flows of biological material through developmental systems; language as flows of information, words, etc.). This fluid substratum is what Deleuze calls the BwO in a general sense.
When put like this the notion becomes clear.
Its useful to note, that the BwO when visualised biologically (which was my first imgainative impulse) has an element of the gothic about it - this is a literary component of Symbolism.
Plane of Immanence - this is derived from Spinoza who has a monist philosophy of substance (God) within which is the world or Nature; thus Immanance; this was a reaction against the Transcendent (God outside of the world); one can classify it as a variation on Emanationist philosophies - other examples being Plotinus or Suhrawardi. The 'plane' in Deleuzes is an allusion to Spinozas 'geometric method', which itself is a tribute to the axiomatic approach in Euclid Elements to plane geometry.
There are dictionaries on Deleuze by Adrian Parr and Eugene Young that might be worth digging through.