I think the easiest way to balance the melees would be to make skills more dependent on all stats...not just the three prime melee stats (str, dex, con)
First rebalance the melee so it is balanced for all race/classes...After rebalancing, it is fairly easy to give reasonable justifications for nearly any change...for example the hitroll one:
Str-based: You have the power to move your weapon around easily, able to change swinging angles quickly, etc
Dex-based: Fine motor skills allow your to slightly adjust your striking angle to bypass the enemy's defense. Superior speed/reactions give you the extra time to make the strike...
Int-based: You superior tactical knowledge gives you insight on how to penetrate your opponent's defenses/armor. You know where and how to hit them. Feints and any other tactical skill...
Wis-based: Using your battle experience, you can easily predict what your opponent will do next. All defensive reactions and their counters are ingrained in your skull. The experience to know when and how to USE any tactical knowledge you've learned...
Con-based: By controlling the energy output of the fight, you can move both slowly AND powerfully along with bursts of speed/strikes. Superior constitution maintains the steadiness of your weapon/arm/footwork and gives you consistency in your attacks, even as your opponent becomes tired...
Power, speed/reactions, knowledge, experience, consistency
Any one of these could be a reasonable justification to use that stat (or a combination of them) for hitroll...
I personaly do not have any trouble with them.
The Stronger, Larger races are more powerful Warriors. It is as it should be.
Smaller races get the Blademaster class suited just for them.
With that said, i think a better balance could be given for Medium sized Warriors.
In the form of the Warrior lore. Some of the exiting lores, or a brand new one could be modified to give them an edge.
YOu play a medium/small warrior, you KNOW what you are in for. You have disadvantages playing giants too. That is like playing a human invoker, and asking them to rebalance so you can use that nifty voker skill to it's max potential. YOu want strong warriors, make strong warrior races.
Also, giving them bonuses for having high wis, int, con etc etc, would you not have to also give them penalties for low stats? Like an elf war is dextrous, but phyiscally weak, and frailer than most, so on top of low hp and limited wepaon choice, you impose a hit/dam penalty as well? A fire giant is a brute swinging a club, but since he is dumb, he suffers penalties beyond arguably the easiest vuln to exploit? It is a sound theory you have, but in practice it fails like toilet snorkles (a toilet snorkel is a patent for fire survival. It is basically a hose you shove in your toilet if you live in a high rise, so you have a source of fresh air to breath, since the water only goes so high in the back)
Your logic would be fantastic, Emp... if it were consistent. Here's what I mean. Let's take a look at which of these combos are typically considered "viable" by the playerbase. Viability does not include cabal, qrace, or equipment choices.
Fire Giant: 3/3 - 100%
Stone Giant: 3/3 - 100%
Storm Giant: 2/3 - 66% (I'm going to say that storm giants don't have the necessary firepower for a berserker, though I haven't played one since the upped strength)
Minotaur: 2/2 - 100%
Ogre: 3/3 - 100%
Gnome: 2/7 - 29%
Elf: 6/10 - 60% (this is giving the benefit of the doubt to an elf blademaster)
Halfling: 2/5 - 40%
Dwarf: 4/5 - 80%
Half-Elf: 4/8 - 50% (I gave ranger and ninja the benefit of the doubt)
Now let's take the averages for our five giant races, and our five non-giant races.
Giants can play any given race/class combo with a 93.2% viability.
Non-Giants can play any given race/class combo with a 55.8% viability.
It would seem to me that giant-sized races have the upper hand.
All that is based on the current system also. To give medium melees a tweaking to make them more powerful takes away the reasons to play the giants. A minotaur zerker SHOULD be stronger than a dwarf berserker, that is just how it works. Also the fact you gave halfers 2 viable options is absurd, we all know one of those that you picked was blm, so that leaves thieves rangers clerics healers. All of which are fantastic for a halfling.
Also you did not nominate storm healer or fire giant shaman as not so viable combos so your throwing the % off there too. And if you picked stone zerk as viable combo, you have to pick storm since their stats are nearly identical, and they get that 10% bonus on water.
You also fail to mention that giants get access to fewer classes. If you want a truly accuracte depiction, you need to do it for every class, or do a class by class comparison to all races.
So you knock my post for flawed logic, then post a flawed display to show the flaws in my logic.
I say we eliminate the current ability score system and implement a much simpler system, and make the game more skill based, then equipment based.
Here is an example of what I mean:
Everyone will still have an ability score, but it will be a much lower number to represent the bonus/penalty they receive to that applicable score.
Fire Giant:
Str: 5
Int: 0 (possibly even -1)
Wis: 0 (or same as above)
Dex: 2
Con: 4-5
In addition, I think that the class choice should also affect those scores, the max still being a 5, but if they choose to be a cleric/shaman, they will receive a penalty to strength and a boost to wisdom.
Or as another idea, making it point buying based on the example above, meaning a max of five points in any one score. Then they divide the points as they like, then apply the applicable bonus' for their race/class combo.
Evangelion I'm not sure why the percentage should be the overriding issue here. Looked at another way, elves, dwarves and half-elves all have more viable class choices than any of the giants, and ogres are the same. The only ones with fewer are minotaur, halfling, and gnome. Your numbers for halflings have also been questioned, I think correctly (barring quest classes). And minotaurs can only be two classes (used to be one). So it's really just gnomes that have fewer viable choices.
Now by viable, you mean capable of being a PK powerhouse. I think this can be questioned too, since the game is about more than that. Some gnomes have been excellent characters even though they were not PK steamrollers. At least one is even in the Hall of Fame.
I agree those percentages are a wee bit scewed to say the least.
Anyone telling me Halflings dont make good rangers is a moron. The same with clerics.
why aren't werebeast involved in this discussion!?!?!?!?
That is exactly my point. You cannot make a table of viable race/class combos without first considering the opinions, pros, and cons of every race/class
Valadis died a long time ago.. let him go... I think you should roll a new guy
see if you can make a Legend out of him, like you did with Valadoooo
Because everyone hates those! 
Fact - alter one letter in hit/dam, and you get hot/dam. Alter that further, and you get, hot damn!
Dey
Why not make every race/class combo viable with custom pros/cons for each. Also I like Celerity's idea, every stats should somehow play a roll in each class otherwise whats the point of rolling any of these totally underpowered chars.
OR
Why not just take away any combo that is not a potential pk powerhouse. Then people will stop complaining that others only roll power combos, since that is all that will be available. /sarcasm
Why not make every race/class combo viable with custom pros/cons for each. Also I like Celerity's idea, every stats should somehow play a roll in each class otherwise whats the point of rolling any of these totally underpowered chars.
I further agree with this. Just gimp the races as if you were to approve someone for an app to it. I don't see why ogres couldn't be mages albeit terrible mages. And do things that would take away certain overpowering factors... like mana shield for ogres. (Rp they can't figure out how to cast the more intricate spells, and lose concentration a certain % of the time because of the slur.) This way, the classes are opened more freely and but may not be as appealing, which would be the effect. Similar perhaps to how Grawrer was "toned" in order to be allowed into warmaster. (No spells or study/assassinate)
You can do that now, we just require an application. Ogre Invokers shouldn't be "normal."
I actually meant make all available race/class combos more viable with custom perks, not open up all race/class combos entirely.
EG - Give gnome warriors and human invokers custom perks to give them a hope in hell.
ps. Grawrer lost spells and study but kept assassinate.
ps. Grawrer lost spells and study but kept assassinate.
For all purposes he effectively lost assassinate for PK. It was likely only left so he could kill mobs easier.
While I almost agree with this. The current balance in the game if we opened up all race/class combos would be lost. I for one would play a storm giant paladin along with the many others. Then every player with an evil would quit, because a storm giant paladin is just ridiculous.