I think the Nord Warfleet is actually quite weak. They're probably designed for landings and raiding as opposed to ship-to-ship battles. Though one could argue a fast longship and a horde of angry nords could capture any vessel on the water.
The Altmer definitely have the strongest in-lore fleet. The Maomer's fleet was annihilated with their King (I forgot his name, Orgnum or something) by the Psijics.
The Reduard's may have the potential still to challenge the Altmeri navy, but their nature makes organizing an army hard enough, to say nothing about a fleet.
The Imperial Navy perhaps was the strongest before the failed Invasion of Akavir. A large portion of the Imperial fleet was lost to storms, still, it'd be hard to believe the Imperials rank anywhere below 3rd, and probably 2nd. While the Akavir business was 300 years ago, so not directly relevant, it does showcase the Empire's potential to field an awesome navy.
Below the Imperials I'm going to have to say Dunmer, actually. Morrowind has a lot of coastline to patrol, and I don't think it's too much of a stretch to assume they have a Navy that's up to the task. Or at least was up to the task prior to the Red Year.
So:
1.Altmer
2.Redguard
3.Imperial (Under the assumption of catastrophic losses during the great war)
4.Dunmer
5.Breton
6.Nord
I assume the Orc, Khajit, Argonians and Bosmer do not field a Navy outside of maritime purposes. Their cultures do not seem inclined toward the endeavor.
Think for a second. Why would you have cannons when everyone in Tamriel can learn spells? Battlemages are routinely deployed on Breton and Imperial ships, and I think we can assume every race's navy, though I can't think of any direct references other than the aforementioned two.