That whole paragraph is full of sexual innuendo that I recognize, and I think the parts I don't recognize have sexual connotations as well. Looking at a bit more context than what you posted, this passage is about prostitutes.
en pleines papouilles agaceries
A “papouille” means touching somebody in a playful way. I'm only familiar with it as applied to tickling children, but the applicability to sexual touching is obvious. An “agacerie” means to try to draw somebody's attention. Either customers trying before buying, or prostitutes attempting to convince potential customers.
Surtout autour de petites nouvelles que ça se lutinait
“Lutiner” means to annoy someone or to touch a woman inappropriately. Here it's clearly the second meaning: passers-by touching the prostitutes, especially the “petites nouvelles” (the new ones; “petite”, in this context, is a disparaging term applied to women viewed as no more than sexual objects, similar to expressions like “the little woman” in English).
On se préparait des petits ménages à la chatouille-barbouilli...
The word “ménage” has multiple meanings. It can refer to a couple or even a nuclear family living together, as in “se mettre en ménage” (to move in together), “revenu du ménage” (couple's joint income), etc. It can also simply refer to sexual activity, as in the English “ménage à trois” (which exists and has the same meaning in French). So here, some “ménages”, i.e. some sexual encounters, are being prepared.
“Chatouiller” mainly means tickle, but it can be a euphemism for sex (about as much so as “tickle” in English), and especially the noun chatouille is often a euphemism for sex. I'm not familiar with barbouilli in this context, but it's a derivative of barbouiller, whose primary meaning is a visual mess, as in something badly painted. A barbouilli is the result of the action barbouiller (like barbouillage, but barbouilli is the form of the noun in my idiolect). It can have various metaphorical meanings, but the general idea is something messy or unpleasant, generally visually. I think that's following the general idea of sex being somewhat messy. A somewhat literal translation could be “one got ready for small get-togethers of the ticklish-messy kind”. Arguably, it could even be translated for meaning as “dirty”, although using such plain language would not respect the tone of the original.
“Chatouille” and “barbouilli” almost rhyme: /ʃa.tu.j/, /baʁ.bu.ji/. This has to be a conscious choice of the author: he could have written “chatouilli-barbouilli” (chatouilli(s) is a noun meaning tickle), but deviated slightly from the pattern. This choice makes me wonder if the sentence shouldn't be interpreted slightly differently, with “chatouille” being a verb and “barbouilli” being its object: the “ménages” are of the “tickle-(a-)barbouilli” kind. This would make “barbouilli” a noun referring either to the prostitutes, to their customers, or both.
Whatever the exact wordplay here, it's about people doing the dirty.
