I sometimes have used the word myself, without ever having sat down and asked myself what do I mean by that exactly. I've used it roughly to mean a coherent body of techniques; I'm not sure if I can amplify much further. "The yoga of adjunctions and mates", "the yoga of the Yoneda lemma and its correlates", and you will find a bunch more scattered around the nLab ("the yoga of 'generalized the' ") if you use the search function. To me, a "yoga" is not quite as formalized (or pretentious) as a "calculus", but it's somewhat in that vein.