What role did the Nine play in the events of TES3? Since the Nerevarine is working for the Empire through most of the Main Quest, I wondered if they were involved behind the scenes. Also, what is the significance of the Nerevarine meeting Wulf/Tiber Septim?

I'm not a huge lore buff, so maybe you could help me figure these out? Thanks.

Walter:

The Blades are directly tied with the Order of Talos (retired members of Blades becoming monks of the Order of Talos), and Wulf just so happens to be the avatar-ish of Talos. So, a lot, if only with Talos.

The Empire will always be tied with Talos.

The "good side" of the Main Quest was moved by two forces, the Blades working on behalf of the Emperor, and Azura the Daedric Prince.

Wulf's appearance has to do with the lore of the Heart of Lorkhan. The cosmology and gods of the Elder Scrolls are complicated topics, but to the best of my understanding, Wulf is an avatar of Talos, the god who is the ninth Divine and who was the mortal emperor Tiber Septim in life. He's also possibly another manifestation of the "missing god" Lorkhan, whose heart Dagoth Ur and the Tribunal steal their powers from. Therefore, he would greatly enjoy seeing these beings lose their stolen divinity. That's the "score" he has to settle with Dagoth Ur, as far as I understand it. Anyone can feel free to correct me if I'm wrong about that, but that's the only way it makes sense to me. Another aspect to complicate it farther is that Lorkhan and Akatosh are two sides of the same coin, and the Tribunal becoming gods created a "Dragon Break", destroying Akatosh for a short while and rearranging the time flow of the Universe, so Akatosh would have a grudge too. And coincidentally, Talos is seen by some as another aspect of Akatosh as well as Lorkhan.

As far as the other Divines and the Imperial Religon in general, I don't think they play much into the main quest. You meet a few of them during the Imperial Cult questline, but that is optional and not tied with the MQ.

It's not clear-cut that the Nerevarine is working for the Empire's benefit (as evidenced by dialog choices when you chat with Dagoth Ur). I view it that I happen to have access to the Blades, who actually aren't really that helpful aside from giving me some funds, info, and training (which I could have gotten anywhere anyway). Plausible deniability.

As for the Aedra - I don't think they really care much about Tribunal, Ancestor and/or daedra-worshippers on Vvardenfell. Or anywhere, really. The Cult seems more political (ethics and political driven) than an actual religion. The Aedra are boring and don't really give a rat's butt except when their own butts are in trouble (Umaril in KotN). Having lots of worshipers is a perk, but they didn't stop Landfall or the dissolution of the Empire. =/ They were more exciting in the Old Days.

Were that the case, then they wouldn't send their avatars to speak to worthy individuals, nor would they hand out special artifacts. They clearly dare, it's just that their involvement is in a far less direct way and places an emphasis on the good character of the heroes involved.

Well, the player does initially take orders from the Blades, but at first, you don't even know what you're working to achieve, and by the time you do, it is I suppose up to you to decide whether you want to defeat Dagoth Ur for the Empire's benefit or for some other end.

But it doesn't look to me like the Nine Divines have had much of a direct influence on the story of Morrowind, while you may encounter some of their avatars in the game, these usually seem to be optional, and are not actually part of the main quest, so I'd assume that the matter of Dagoth Ur and the Sixth House was not something they felt the need to directly intervene in, the main divine influence on the Morrowind main quest would be Azura, whose involvement is not hard to notice.

how did the Nevarine get out of Jail? A moth priest told Uriel the myth. Why did the Moth priest do that? Kyne showed him it in an Elder Scroll

Did she? Where is that stated?