There is no order to most of the last half of the Main Quest. I've indexed it by trial, but that's just for my own convenience. The only "requirement" (see the Hiccup page for why it's not) is that you get yourself named "Nerevarine" by each of the four Ashlander tribes and get named "Hortator" by each of the three Great Houses. The order in which you do it (or if you do it at all) is entirely up to you.
By this point in the game, being named Nerevarine by the Urshilaku is simply a matter of asking. Sul Matuul will want you to talk to you about "Need" and "Duty," but that's about it. You get a set of enchanted teeth (Constant Effect: 10% resistance to paralysis) and a 2-point boost to your overall rep.
Congratulations! You're 1/4 of the way done with the fourth trial.