Just realized I forgot to respond to this. My sincere apologies, and I have actually given some thoughts to this over the various drives I have made across the state over the past week, so I'll just take it section by section with how I've adjusted for the various races with the current mod I use to decide battles. Upon further review, the mod may not last, simply because I've been discovering that the AI has no clear idea how to actually use things like the autogun and zeppelins which can actually do battle. It makes me sad, but that is the hard truth, though it still works for battles without those things.
Humans: Well, based on the manual for Warcraft 3, it implies that the human armies deteriorated during peacetime to a limited degree, which could imply that as a justifiable reason for why human footman and orc grunts were no longer equal in combat. As for healing, in Warcraft 1, it was done by the clerics, whose name I have kept here for that reason. In Warcraft 2, the clerics were said to be disbanded and their duties taken up by paladins, and that's certainly the case in gameplay mechanics. This was retroactively changed in Warcraft 3, in which they stated in game that the paladins were created to serve alongside priests, which is more in line with what World of Warcraft itself actually presents. I personally have chosen to adopt the Warcraft 3 approach, and believe that clerics and paladins will continue to serve together, and paladins (if they are formed) will be an elite, almost heroic unit for each one, requiring a knight as a requisite for training. As for magic, if I was to stay 100% true to the various Lore presented, Stormwind would have a unique spellcaster called a Conjurer. I made the decision to remove this class, because later incarnations of the world would have their duties and abilities overlap with the warlock. The generic term "Mage" works best to cover the magics available to the casters of the world of Azeroth.
Orcs: They are known to be one for one stronger than the humans in Warcraft 3, but there is a reason why that occurred to me. Those that were capable of fighting by the time of Warcraft 3 (25ish years after the events currently in the NES) are those who both still had the spirit and ability to fight. Therefore any who had survived to the point of Warcraft 3 certainly were the prime, while the humans had a period of decadence and peace after the Hordes were defeated in the Second War.
Elves: I fully agree with your assessment of the elves.
Dwarves: No disagreement here either, as dwarven settlements are built mostly as major strongholds which can be easily sealed off from invasion. Therefore siege and defensive war are the only things known to the dwarves in the sense of warfare. That's why the Dark Irons continued to hold multiple levels of Blackrock Mountain for decades, despite the Horde having defeated them and overrun them in the field, as well as establishing the upper levels of Blackrock Mountain as their own citadel, even with the dwarves consistently harassing them from below. Similarly, Ironforge was able to hold out indefinitely, having ample stockpiles in the bowels of the city, and essentially managed to hold the entire population of Khaz Modan excepting the gnomes for a long period of time.
Gnomes: In Warcraft 2, and that time period, based on what we know in the manual, gnomes were still very nearly creatures of myth to human kingdoms. They would rarely be seen wandering around, and the gnomish-goblin rivalry is said to be ancient in origins, though lord knows why. Due to the concealed nature of their capital, Gnomeragen, they were never directly threatened by the Horde over the course of the Second War. Other than that though, you've nailed it, though their warriors are the weakest around, relying mostly on support weapons like rifles and inventions to supplement their smaller strength and ability on the battlefield. Of course, due to the inherent instability and eccenticity of the gnomes, most of their stuff is just as likely to backfire as work properly.
Goblins: Stronger than the gnomes, they still have all the basic same things about their society. The key difference though, is that Goblins gained their intelligence via a rare mineral found only on Kezan. This mineral has begun to run low, meaning that while goblins are still clever, their intelligence is in a constant state of decline, which is why half of the time their inventions fail and blow up their creators.
@EQ: Thanks, this does explain a lot. Im no longer ing now, but I think this has expanded into a discussion that would be beneficial to the nes.
Based on my understanding, with the games and most of the books in mind (theres only a few that I havent gotten to). If other people have an opinion, please put your two cents in.
Humans: Probably one of the most straight forward militaries, but the lore is still contradictory in some ways. Humans (Azeroth, Lordaeron, and Stromgarde in particular) have the largest/strongest paleskin armies, however the Horde outnumbers them, especially so in the First War and early Second. In the first two games, orc and human warriors/footmen are equal, but Ive always took this as a gameplay mechanic and not lore savvy. WCIII was the first time they tried to integrate a difference in their units. The books are kind of consistent in portraying humans as either a tad or a lot weaker than orcs, with their armor and discipline making them able to fight the larger and more powerful orcs one on one. In the battles, it was the armys tactics and discipline that they used to try and out fight the weight of the Horde. Mages, as you said, were big on the healing, but that role has largely been taken over by priest.
Orcs: Orc battle strategy is to use their sheer numbers to try and overwhelm Human defenses, and to flood holes in shieldwalls to break up the Human units and smother them. When the human defenses are too strong, they try and skirt around it, for instance after the initial invasion or Lordaeron the Horde couldnt break the Human army at the beach, so they turned east to the Hinterlands and further east still to QuelThalas until they were finally able to slip the Alliance in Alterac and go for the Capitol City. When they dont have the numerical superiority, or are unable to out maneuver the Humans, they start to lose. Azeroth was able to hold the Orcs off at the beginning of the First War with relative ease due to the small number of clans coming through the Portal at that time, and at the end of the Second when the Horde had finally spread themselves too thin with troops Khaz Modan, the Hinterlands, QuelThalas, Alterac, and Lordaeron as well as Guldans rebellion, allowing the Alliance to beat each section in detail.
Elves: Elves have smaller, yet more disciplined army than the Human and use the same tactics; however in the books the main army stays home until later in the Second War. The Rangers is their main offensive arm, being able to hold the Trolls at bay plus being the best scouts/light infantry in the world. Archery is the rangers main method of warfare (see WCII) as is their ability to fall back when they are outmatched. Rangers are weak when enemies can close in on them and break their line of retreat.
Trolls: Lore is holistically contradictory on how strong these guys are. In the games, as stated, they are crappy melee units on the most part. The books, on the other hand, often compare Trolls to Ogres. Doomhammer states in Tides of Darkness that they are strong as Ogres but smart as Orcs and in the Last Gardian Prince Lane, Lothar, and Mediev are ambushed by a lone Troll who completely pones Lane and Lothar strength wise. Trolls do rely on ambush as their main point of attack, using the trees as staging areas and tactics very similar to Elven Rangers. Berserkers are similar to Orcs in that their main job is to break enemy lines, allowing their brethren to swarm holes and destroy unity.
Dwarves: Kings of the defense. Even in the War of Three Hammers, the main fighting was sieges and counter sieges. Skilled at using gunpowder weapons and mountain defenses to make the most of their small numbers. In the Second War, they were able to hold Ironforge even after losing everything else. Heavily armed Dwarven warriors are used to break siege lines, and hold walls. Dark Iron dwarves, on the other hand, use ambushes and magic to make up for their even smaller numbers. Wildhammer Dwarves use their griffin riders and their stromhammers to defeat larger armies unused to fighting aerial units.
Gnomes: Greatest technologic developers in the world. They use their technologies to shock and awe their foes, but are so small that they have to heavily rely on their Bronzebeard allies for protection.
Goblins: To be honest, not too sure but I believe similar to Gnomes.
('cept for the major issue of losing Medivh I guess, that was my bad, panicking after the first two sieges). 
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