To engage in "Woggery" is to practice the dark arts of skullduggery, manipulation, and the propagation of spurious "facts" in order to aidone's argument. It helps to also be of Greek/Cypriot heritage and be of hirsute disposition.
I was completely buying into what he was saying, but then noticed (as he offered me a slice of halloumi) that he was engaging in the dark arts of Woggery.