The Argonians are fine. The only place Red Mountain REALLY impacted was Vvardenfall, which is in the process of being rebuilt. Look up "The Red Year". What is your source on Hammerfell being occupied? Last I checked, they sent the Dominion packing. As far as Cyrodill, at most they might have a few agents and ambassadors to make sure the treaty is upheld, but not an occupation of any real scale. Also, the Imperials state multiple times that they're getting ready for war, and the conflict in Skyrim is just a prelude to the main event.
The Stormcloaks are certainly tough, but they have nowhere near the manpower or the money of The Empire. Even at their absolute best, and assuming that they could present an actual threat to the Dominion, that threat still isn't as large as The Empire proper. If it wasn't for Alduin, Ulfric would have had his head removed.
No notes on argonians taking side in the great war although Black March is part of Empire. Most likely because they also fought Daedra during OC. Many, many Dunmer fled from Morrowind, repairs started, but thats one thing. It's way more difficult to raise an army when your population is cut half. Thank you for correcting me about Hammerfell, though, their ties with Empire are too bitter now. Empire can't really count on them in the upcoming Great War. After all, redguards were annoyed with them after they accepted WGC, hence why they continued to fight. Some really hard negotiations would need to take place, it was long gained trust that was betrayed that day. Ironicly, I see better chances for Ulfric and Hammerfell to make an alliance, since Ulfric was also struck hard by WGC, rather than Empire and Hammerfell who are on bitter relations.
Stormcloacks are getting ready for war too, right after you finish their quest-line. And if Hammerfell could hold their ground, why can't Skyrim?
Aldmeri Dominion are organisation that never takes action unless it's completely, and only in their benefit. They started Great War, naming him First War with the Empire, most probably implying that they planned more wars to take place, from the start. Also, the solider's they planted in Cyrodill are completely enough to keep their hands tied. Emperor can't do anything without their knowledge.
I still believe Thalmor will win next great war, and what they do will trigger the events of TES VI. "Mortals who dare play God must pay steep price". I expect Divine retrobution to Thalmor in next TES games, but that remains to be seen.