Strength: Increases Natural Damage
Agility: Increases Natural Evade
Intelligence: I think that Int. Increases spell accurcay on Status/Death Spells...
Vitality: Honestly, I dont know what it does... Hp gain depends on the player class.
Luck: Better chance to run away, but im not sure about Cricital Hit %... I think Cricitals are based on Hit%

Hit% seems to be scripted and increases little by little as it goes on...

Multiple hits depends on Class and their level.

High and Low Hp gains is somepart scripted and somepart chance. On some levels you always get a High Hp gain while some others you always get a low hp gain. The rest is Chance Where you can get one or the other... This has nothing to do with vitality, but rather actual luck (Not in game luck).

I know this because I tried the "restart if no High hp gain" trick. Some parts that happens

Stats are completely randomized unless your a certain class. ie. Fighters always get S, Thief's L, Black's V, Mages I. The Red Mage however, is the only one that has all 5 stats randomized but always gets at least one type of stat per level.