How to calculate battles:

Hit: (Weapon Hit) + (2 x Skill) + (.5 x Luck) - Opponent's Aviod

Avoid: 2 x (Speed - Weapon penalty) + Luck

Weapon Penalty: Weapon Weight - Con (*Note: Cannot be lower that zero*)

Damage (MT): Strength + Weapon MT - Opponent's Def/Res (depending on the type of attack)

Critical: (.5 x Skill) + Weapon Crit - Opponent's Luck

Attack Speed: Speed - Weapon Penalty

Double Attack: When your AS is at least 4 greater than your opponent's.

Stealing: For a thief to steal, the thief's speed must be greater than the enemies speed.

Hidden Items: Luck x 2 = % of getting hidden item when on the designated square(s).

Rescuing Units: When rescuing another unit, SPD and SKL are lowered by half for the rescuer.

Devil Axe: 31 - Luck = % of criticalling self.

Experience:

If didn't kill foe: 10 - 2 x (Your Level - Opponent's Level)
If killed foe: 20 - 4 x (Your Level - Opponent's Level)

Staff Experience:

Weapon Experience: You receive 1 WEXP for every attack you make on an enemy, regardless of weapon. Below is a chart comparing the rank to the amount of WEXP required. Remember that once your weapon level ranks up, your WEXP resets to 0.

Note 1: Fatal hits give double Weapon EXP.
Note 2: Weapon EXP is gained even if no damage is done or the attack misses.
Note 3: No Weapon EXP is obtained when using the Light Brand (indirect), Runesword or Wind Sword (indirect).
Note 4: No Weapon EXP is obtained when a weapon or staff breaks.
Note 5: The maximum Weapon Rank for non-promoted characters is A (Weapon EXP towards an S Rank cannot be obtained).
Note 6: The maximum Weapon Rank for promoted characters is S (Weapon EXP towards an SS rank cannot be obtained).
Note 7: Characters can only have one S Rank (or SS rank at mater rank)
Note 8: Magic users lose weapon uses when attacks miss.

Other Important Things to Note:

• Promoted vs. Unpromoted: Exp x .5 for promoted unit / Exp x 2 for unpromoted unit
• Triangle Advantages: -15 Hit% and -1 MT for disadvantaged
  +15 Hit% and +1 MT for advantaged
• Reaver Weapons: Reverses Weapon Triangle, -30 Hit% and -2 MT for disadvantaged
  +30 Hit% and +2 MT for advantaged
• Weapon Flash: Weapon Power x 3
• SwordSlayer: Reaver + flash on Mercenaries, Myrmidons, and their promoted forms

How to post a battle:

Here's an example with my character, a Myrmidon whose skill is "Wrath" (Boost critical by 30 when at less then half HP):

Adam
HP: 19
Mt: 7 (x2)
Hit: 100
Crit: 5

Brigand
HP: 24
Mt: 10
Hit: 47
Crit: 0

Adam hits; Brigand at 17 (RN --, 89)
Brigand hits; Adam at 9 (RN 18, --)

Adam Activates Wrath!

Adam Criticals for 21; Brigand falls (RN --, 7)

Assuming Adam is at level 1 and the brigand is at 4, this would be the status bar following the battle:

Adam | lvl 1 | HP: 9 | E: 32 | WE: 1 | Wrath

Terrain Bonuses:

Different types of terrain give different bonuses when a character stands on them. Pegasi and wyverns are not affected by terrain, but all other units are. Here is a list of all the terrain that give bonuses:

Other Information About Terrain:

Fortresses, gates, and thrones heal a character a certain amount of HP each turn they stand on that tile. The formula for how much HP is: Total HP/10 (All decimals are rounded down).
Villages and houses can be visted during a battle, and an item is recieved.
Fire tiles cause a player to lose -10 hp when stood upon.

Weapon Stats:

* = Half user's MAG stat

Just a bit of offhand info to be added as I think-

AI goes for most damage per hit primarily. Then it looks at lowest HP. Then weapon triangle, hit chance, and finally crit. Damage to self isn't factored in unless all of these are the same. If everything listed is identical, RNG decides.

All of that applies AFTER determining whether on not the defending unit can counter. Obviously, can't counter takes priority.