I think a a lot of people, myself included, think the Aldmeri Dominion (AD) are some extreme badasses who are extremely powerful and can defeat anybody and anything.

But how strong are they exactly? Sure they took the Imperial City and "won" the Great War, but a very weakened Empire took it back and caused the AD to stop fighting. In a way the AD was not to keep fighting either, else they would not have proposed the White-Gold Concordat. Not to mention they was defeated by Hammerfall, a lone nation.

Also what do Bosmer and Khajiit think of the AD and Thalmor? Do/did they fight for them?

I honestly don't think the AD is that strong and the Empire could defeat them.

The Empire probably could repulse them again. The Redguards did.

But to repulse them is not to permanently defeat them. They'd just turtle up again on Summerset and rebuild again, sending out their spies and provocateurs to soften up their enemies. No, truly defeating them will require kicking in their front door on Summerset, taking their capital, and then hunting them down like they did to the Blades. And that will require a concerted effort of all those against them. That's something the Thalmor have been actively working to disrupt: Divide and Conquer.

One thing you have to seperate is the Aldmeri Dominion and Thalmor, they are two seperate entities. The Thalmor are a minority faction that are currently in power, and they are very smart politically. As for the Bosmer and the Khajiit, well the Bosmer obviously fight for the Dominion because they are part of it. The Khajiit do as well because while not part of the Mer association, they are client states of the Dominion.

As for who could defeat who? I don't think the Empire could defeat anybody right now. However, I do believe the Thalmor can be defeated. Doing so though would most likely only strengthen the Dominion because the hated faction would no longer be in power.

The Redguards did not repulse them, they were in a stalemate and the Dominion left.

The AD's main mistake in their attack was that it was too broad to be conquered all at once. However they were successful with the WGC in that that Hammerfell left the Empire, weakening the Empire's strength even more.

I imagine their navy is still one of the strongest navies in all of Tamriel since at one point the Alinor Naval power was the greatest one which would mean they can easily defend the isles.

The Dominion is not an all-powerful juggernaut. Their most powerful asset is their espionage capability. Their agents create disharmony in enemy states, so that the Dominion proper can either walk in and take over after a period of chaos, or can otherwise take advantage of the mess for other reasons. Militarily, I would say that the Dominion and the Empire are--or at least were, during the Great War--somewhat evenly matched; the difference between them, and the great progress of the Dominion in the early stages of the war, came mostly from the fact that the Dominion was prepared for war while the Empire was not, the Dominion had intelligence regarding the Empire's movements while the Blades were all dead, and the Dominion had crushed dissent while the Empire was, in some respects, divided against itself. Once the Dominion's enemies had regrouped, they were able to drive the Dominion armies back and regain some measure of power in their own territories. Even so, it should be remembered that defensive wars are not as difficult to mount as invasions, for obvious reasons. It's likely that any attempt by the Empire to invade Dominion territory would involve lots of Legions being slaughtered in the Valenwood jungles and lots of ships being sunk by Alinori Sunbirds, just as the Empire and Hammerfell were able to repulse the Dominion's invasion of their territories (moreso in the case of Hammerfell than the Empire, it must be said).

In short, the Dominion has an adequate army, but the groundwork has always been prepared by the spies and agents of the Thalmor; if the Dominion relies on its military for outright victory, it will likely be sorely disappointed. Which, of course, is why it has never done that, nor do I expect it to suddenly throw away two hundred years of successful strategy for the sake of a second Great War.

I agree that the Dominion doesn't have more muscle than the Empire. First, the Altmer lean toward magical attacks, the Bosmer to bows and stealth, only the Khajiit have an effective mixed force (the lore Khajiit, not the little sneaky cat people in game but also the giant funking sentient tigers). Also, the Thalmor are a minority government, effective but without a wide enthusiastic base (although what we know is filtered thru Imperial sources). The Bosmer and Khajiit probably didn't field all of the forces they could have- even given that both lean heavily to guerrilla tactics, it might not have helped much in the main assault, but teams of Bosmer and Khajiit guerrillas rampaging over Cyrodiil, attacking cities far from the front and harassing the legions moving in from the north would have been highly effective, but we see no mention of it in the (terribly brief) account of the war.

I am going to speculate that the Bosmer are still divided, thus losing half their strength from them, and the Khajiit... well, it is hard to herd cats ;p

My opinion is, if the Thalmor weren't such raging arses, they could more effectively create support for their Mer uber alles plan. Altmer battlemages blasting away with destruction spells, Bosmer archers sniping and using beast tongue to take control of the horses the legion officers are riding, and oh yes tigers with warriors on their backs come charging in from behind... I don't know how long the legions could stand against that.

They ain't called Old Mary for nothing.