Theory on HP and Strength (some spoilers)
A lot of things in the Final Fantasy universe (or any RPG, for that matter) don't make a whole lot of sense. Among those are two common character stats - HP and Strength.
Many people associate HP with a character's "health." When Tidus has full HP, he is in perfect health; when he dwindles down to 50 HP he is on death's door; and when his HP hits 0 he dies. However, too many things don't make sense with health. Cloud has about 300 HP at the start of FF7. The first enemy he encounters, a Shinra guard, shoots him in the face with a machine gun and inflicts 7 HP damage. 7! You would expect a machine gun would do more than reduce your ability to live by 3%. To make matters worse, this guy's buddy runs up and smacks Cloud in the stomach with his nightstick, and inflicts more damage than the machine gun. What gives?
That's why I say that HP is more of a representation of endurance rather than health. When I say endurance, I mean the character's ability to block, evade, and/or absorb attacks. What does this mean? Let's go through the FF7 scenario again. The guard that's supposed to shoot Cloud - he's not very good at what he does. He's probably some rent-a-cop being paid minimum wage to guard a train station. Maybe he even has poor eyesight. Needless to say, he's not a very good shot. So he fires in the general direction of his spikey-haired assailant and misses. Cloud does have to exert some effort to get out of this guy's line of sight, so his endurance is going to decrease. Obviously, he can't keep dodging bullets all day, but with this guy's aim, he could last for a good amount of time. A stray bullet or two might graze his skin, causing him to lose a lot of endurance - this would be a "critical hit."
So the second guard gets tired of Ray Charles doing the fighting and decides to take matters into his own hands. He runs up and plants a nice smack in the middle of Cloud's stomach with his nightstick. Cloud, of course, has rock-solid abs, and is able to absorb most of the blow my pulling back and flexing his stomach. At most, it might knock the wind out of him for a second or two, hurting his ability to absorb more of those attacks. As Cloud's endurance decreases, he becomes more tired, and is able to block, evade, or absorb fewer and fewer attacks. Also, more powerful enemies will make it harder for Cloud to dodge its attacks. So if an enemy inflicts 295 out of 300 HP damage, Cloud still dodges the attack - but maybe he had to dislocate his shoulder and use his face as a shield to do so. Don't ask me - Cloud doesn't seem like the most mentally stable person around.
"Aha!" you might say, "What about the evasion stat?" Well, my loud friend, let me tell you what about. Evasion, according to my theory, is simply the percentage of attacks the character will be able to avoid effortlessly, with no reduction of his or her ability to avoid further attacks. So when Locke "evades" an attack, he is doing almost nothing to avoid being hit - maybe he's hiding behind a tree. This is why "evasion" occurs on a percentage basis, while "hits" happen every other time.
So what happens when Quistis loses all her HP? Quite simple - she passes out. Only a special "Phoenix Down" or a Raise spell ("Life" is a misnomer in this case) can get her back into the game. Even then, she's going to be groggy, and her HP will thusly still be low. This allows us to side-step the age-old question: "Why didn't they use a Life spell on Aeris?" Answer: "Because she had a large sword run through her spinal column, silly."
On to the next subject: strength. For starters, strength is all fine and dandy when it comes to melee weapons. Obviously, it takes some physical strength to wield any sort of sword, axe, stave, dagger, katana, spear, book, paintbrush, rod, harp, or accordion. Where this theory breaks down can be centered on one character in particular: Irvine Kinneas.
Irvine is a sharpshooter by trade, and a self-proclaimed ladies' man. Some would just call him a pompous ass, but I digress. What makes him such an an anomaly to the idea of "strength" is that when his strength stat is higher, he will do more damage. This is where your brain should screech to a halt and scream "DOES NOT COMPUTE!" For the most part, we all know how guns work. Pulling the trigger harder will not make a rifle any more powerful (try all you like, though).
Fear not, brave citizens, for I have the answers that you seek! You see, "strength" is not really a measure of physical strength, per se. Instead, it is a measure of a character's battle prowess. So when Irvine's strength increases (God, I hate junctioning), he is really getting better at fighting in battle - in other words, his aim is getting better. This means that he will inflict more damage on his targets. Or, if you subscribe to my HP theory, he's making it much harder for his targets to dodge his attacks.
Wow, that was long. Well, time for me to go recover whatever I have left of my life.