Thanks, André, that's helpful. This:
In general, if a topos $mathcal{E}$ classifies the models of a geometric theory T, there is another topos $mathcal{E}$ which classifies variable families of models of T: it is the *bagdomain* of $mathcal{E}$ introduced by Johnstone. See the Elephant vol. I Proposition 4.4.16.
is particularly good. I knew about the bagdomain, but didn't connect it to my question. However, I think I want a non-transitive torsor to be a right G-set with a free action, but which is also inhabited. This means passing to a subtopos of [X, Set], where X is as before the category of finitely generated free G^op sets. Looking at the calculation I made before, I think I got it wrong. I must pass to the topology generated by making 0 ----> G into a cocover in X. But then I must also make every pushout of this into a cocover, and every composite of such pushouts into a cocover. So, in the end, I think the classifying topos should be Sh(X^op) for the topology whose cocovers are the coproduct injections in X. In other words, I take the Lawvere theory of G^op-sets, and take sheaves on it for the topology given by the project projections. Richard [For admin and other information see: http://www.mta.ca/~cat-dist/ ]