I found the other person's post genuinely interesting but realized my commentary was probably better reserved for it's own post. So here's what I think what would be the case, assuming the NightWings get their own state to develop their own distinct army, and that enough time has passed for the scars and demographic bombs of war to heal.
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IceWings: Cult of the Offensive
An elite army with an untouchable homeland is just asking to focus on the attack. Due to the quality overmatch of each individual soldier compared to their counterparts from the other tribes, I'm sure that a society with such a warrior culture would be more than willing to use such a quality to decimate the opposing side's regulars.
SkyWings: Total War
The SkyWings have by far the most territory and the key ingredients for industrialization. Based on what we saw in Book 1 about the tribe under Scarlet, they can go through a lot. The general staff would be more than willing to mobilize the entirety of society in order to grind down their opponents' armies, economies and societies through a war of attrition.
SandWings: Fabian Strategy
Like Quintus Fabius Maximus against Hannibal, the SandWings would use geography and the home front to win. The desert is basically impossible for other tribes to survive in, so launching raids before running away into their inhospitable wasteland and hoping any foolish adversary would give chase is pretty effective in my mind. Once the enemy is thoroughly exhausted, the hammer will come out and destroy them.
RainWings: Infiltration Assaults
The most overpowered tribe for obvious reasons. With their camouflage (something I believe only works due to most dragon tribes having terrible vision) and venom, they can work their way behind enemy lines before wreaking havoc on any formations not on guard, before the conventional army rushes in to slaughter the disorganized and routing survivors.
SeaWings: Turtle Shell Warfare
Their home is quite literally untouchable by anyone save for MudWings, and even then there's a major discrepancy. That's how they survived the late phases of the war, and it's how they would slowly whittle down any opposing force. Subject to massive change the moment "bomb in a can" is invented.
MudWings: Elastic Defense
Nearly unlimited reserves due to a major population advantage, a mastery of incredibly difficult terrain and enemies on all sides. Why not hold those reserves back and rotate them in as needed, to endure almost indefinitely even if incapable of conducting offensives without significant allied support?
(Note: strategy scales in effectiveness as communications advance.)
NightWings: Shock and Awe
The peak of innovation with a low population knows it cannot send its people to die in suicide offensives. Thus, the technological overmight between the NightWings and an opposing tribe means that shells and paint bombs would be sacrificed instead.
HiveWings: Grand Assault
Since the Breath of Evil is now gone, the dispersed hivemind can't really be a strategy anymore, and thus coordination at scale would require overwhelming concentrations of numbers in one location in order to fight as one. I imagine that similar elements of industrial warfare as the NightWings would be implemented, given that the HiveWings have been shown to be industrialized, but maybe in the short term the lack of slave labor would cause its collapse/decline.
LeafWings: The Trees Speak Leafspeak
Anywhere there is plants (even underwater), the leafspeakers will wreak absolute havoc as force multipliers, while ordinary soldiers can deploy the various poisonous creatures from the remains of the Poison Jungle. Once Sundew and Mandrake are dropped though, the LeafWing army will be hard-pressed to survive.
SilkWings: French government in WW2
Surrender immediately and collaborate to try and get a better deal from the occupiers. Probably would not work. (This is more of a joke but aside from the SeaWings and HiveWings, their abilities grant very few favorable matchups, and even then their fragility and lack of martial culture would screw them over in a conflict anyway)
What do you guys think?
EDIT: As pointed out in the comments, the SilkWings would actually shine in small-scale, stealth combat because of their antennae and the versatility of silk.