From Oblivion, it looks like the Niben river and the Topal Bay are seperated by some swamp thing. So would all sea-faring cargo bound for the IC and Bravil from say, Senchal have to take one ship to Leyawiin then transfer to a second ship already in the Niben River, or is it just a flaw in the way Oblivion depicted that area?

Considering http://www.uesp.net/wiki/Oblivion:An_Unexpected_Voyage, I would say yes.

That, and also, in the concept art shown before Oblivion was released, Leyawiin was actually depicted somewhat differerently, and it looked like the river actually flowed through it, instead in the game it blocks the river and there are a few ponds in it, most likely, it was simply an oversight on the designers' part, and actually, the river does flow into the bay.

It's almost as if Oblivion is non-canon to the rest of TES lore (or should be).

A sentiment shared by many

What you saw was an extremely low tide at sea during the dry season of Cyrodiil. Normally during this season the water becomes so low that the Niben actually flows inland, providing a most opportune moment for Cyrodiils merchants to return home. Yet this time the water was low enough to expose the shoals of Leyawiin. Quite typical really as during any other period Leyawiin stands to make a fortune using mules to lift the ships across the shoals.

Man, I miss those old weaselings.

There's two separate questions here.

Does it flow? Yes, even if it's through a swamp, or partially underground - pipes under the town?

Is it navigable? Not in the Oblivion period, but that doesn't mean it never was, or won't be again. Dredge out that silt, and it'll be back to normal again.