The Edda river begins in the Beor Mountains and elfland. It's actually two rivers joining up forming one (seemingly of equal size which probably happens in the real world though I don't know any examples). The flow makes sense if we assume that large body of water isn't the ocean and instead is just another lake. That would give it a south easterly flow. It would also mean the river flowing form those lakes is yet another separate river that becomes it's tributary. This direction of flow also makes a bit of sense considering we know there's a coast roughly to the south while where the north ends is mostly unknown.

Here's a mock up of the idea I'm suggesting.
https://i.imgur.com/c84b5eS.png