The majority of the Altmer military is mages, generally in the form of battlemages and spellswords. It’s also likely they have a strong infantry, supported by enchantments, potions, and poisons. Destruction mages take care of enemies at range and are trained in melee to be competent spellswords. Very focused on tactical superiority rather than raw power. This is interesting because the Imperials would also have a focus on strategy and tactics, though evidently, the Dominion’s strategy won out over the imperials. Perhaps more credit is due to the tactics of the Bosmer and Khajiit forces but until we have more information on the actual war, it’s hard to say
Black Marsh is a harsh land to outsiders and the Argonians have grown to use that to their advantage. They know the terrain better than anyone and that is well-suited to their guerrilla tactics. They’re very fast and with the ability to breathe underwater, could remain undetected for long periods. Their knowledge of the land comes into play when making and using poisons against their enemies, often targeting supplies rather than engaging the enemy directly. Overall, don’t fuck with these guys.
The well-known knights of High Rock make up the majority of the Breton military. Knightly orders likely work well together as a unit and the units are together under the command of their lord. Their strong cavalry is supported by conjuration and restoration mages, keeping them alive and providing a small infantry force. It’s unlikely that the Bretons to go to war often except under direction from the Empire.
Like the Argonians, the Bosmer make good use of guerrilla warfare, especially in their homeland. They don’t have much of an infantry force, so their ranged forces sneak about in the forest, striking quickly and disappearing back into the trees. Their armor is light and designed to move with them to allow them to climb and dodge very well. Bosmer on the whole are well-known for their ability with a bow, and the Bosmer use that to strike suddenly at a range, often taking down enemies before they realize.
Most of the Dunmer army is supplied by House Redoran and reinforced with mercenaries. Therefore it can be concluded that Dunmer tactics focus on small forces using heavy armor, spears and long blades, with a healthy dose of destruction magic. Likely this would be not too unlike the landsknecht forces though on a significantly smaller scale, and with much less color.
Imperials have been shown to be essentially fantasy Rome. Their shields closely resemble the Roman scutum and would be used that way. Imperial tactics are highly organized and focused on defensive shield walls with blades and maces, and supported by spears and the main offense. It’s highly likely that the Imperials have a system of mandatory military service with compulsory training, and therefore everyone knows the basic tactics and how the Legion operates. It’s also possible that in Imperial towns in other provinces require similar training.
The Khajiit rely heavily on their agility and speed in combat. Their natural ability with hand to hand combat gives them an edge in a grapple and a short blade is an excellent weapon to use in a situation like that. They would use combat techniques not unlike Italian dagger fighting. They make great support fighters for other infantry forces.
They’re basically fantasy vikings so it’s likely that their tactics work similarly. Their weapons are essentially viking weapons which would make shield wall tactics very viable, especially with large, round shields, however that is only for hold and city guards. The interesting thing is the way their governing is set up, with a system of jarls, thanes, and housecarls. Such a system ensures that housecarls train to work well together and with their thane, but its unlikely that thanes of even the same hold train together often if at all, much less from different holds. This means that Nordic tactics would have a focus on small, experienced forces made up of strong individual fighters that work well together, supported by more organized city guards.
Orsimer train with weapons starting at a young age. They rely heavily on themselves in combat, with very little focus on tactics or teamwork. This means they are trained to keep themselves alive with shields and heavy armor since the attitude is that no one has your back but you. The end result is a group of disorganized, but fearsome warriors, each capable of taking on multiple opponents at a time.
For the Redguards, it is likely that the majority of their military force is formed of cavalry, since that historically was the main use for a scimitar, which are common weapons in Hammerfell. The curved shape of the sword allowed a rider to strike and continue to ride without getting his sword caught. This cavalry force would be supported by a fearsome infantry serving as an anvil to the cavalry’s hammer. The infantry would be outfitted in heavy armor with shields and blades while the cavalry would be comparatively lighter with medium armor and swords to allow for more mobility on horseback.