[Eönwë]

For all seas, lakes, rivers, fountains and springs are in his
government; so that the elves say that the spirit of Ulmo runs in all
the veins of the world.

Originally Posted by Legate of Amon Lanc

Well, at least for the Sea of Núrnen, my personal belief is that this was a place where he really didn't have much, if any influence. Not only was it as close to Sauron as it could, but it was also an inland sea with seemingly no connection to the Belegaer. So no rivers, no flows connecting its waters to the Great Sea - it was probably a lake whose waters, from most part, evaporated and that was the only way the water got away from there.

But if Ulmo is the Lord of All waters, would he be able to control rain and such? Would the spirit of Ulmo run in all the actual veins of living beings? Would that give him absolute control?

Originally Posted by Ibrîniðilpathânezel

I have wondered if this is because of their aversion to something as inherently clean and pure as free-flowing water, or if it still contains traces of Ulmo's presence, which they might well have reason to fear.

Wouldn't the two be connected? Water is "unmarrable" (well, almost) because of Ulmo. Ulmo's spirit can live on in water without it actually having to "contain traces of his presence" as you put it.

Originally Posted by Legate of Amon Lanc

He was not afraid of water. Whether the water did have any effect on him is a completely different question (and in the end, it indeed had... ). He may still have felt a little dizzy or uncomfortable in the water, like somebody who has an allergy or something, but he was not afraid - for what reason in particular, we don't know. He may have been simply more rational person than the others

Considering that his main weapon is fear, you might have something there...

As for the eagles, I think that most of what they did they did themsleves, but I agree with Legate in that they probably got a little nudge from Manwe in things such as the Black Gate.