Commanders have their own stats, their troop stats and their command abilities.
Commander stats (attack, defence and strikes) : used when calculating damage done in battles (and the chance of damage being done to them). Strikes is the maximum amount of attacks (and maximum potential damage) that a commander can do, most commanders have a relatively low number of strikes and will inflict 10 or less damage to enemy troops. They are mainly useful when attacking demons or when using "snipe" skills to damage commanders directly. When attacking commanders, commanders only seem to attack a maximum of 6 times, even if the Kaijuu prince has 200 strikes.
Strikes can vary quite a lot, Kaijuu Prince with 200 strikes can attack up to 300 times against enemy troops and a much lower amount. This seems to be fairly random. The number of troops killed is dependant on the commander attack vs the target unit's defence. With 8 attack vs 8 defence, only about 10% of the strikes will cause damage. Once you reach a certain number of attack over enemy defence, more attack ceases to make a difference. At 20 attack vs 8 defence (super hannies, one of the strongest regular enemies in the game), adding a +2 attack item to the commander makes no difference in terms of damage dealt. If the attack is high enough, it can actually cause more damage than the number of strikes (e.g. 250 damage dealt with 220 strikes).
Attacks always seem to do a minimum number of damage regardless of how high the target's defence is. This is most noticeable when commanders are being directly attacked by a large number of low quality troops. Because most commanders have very low number of strikes and the ones that do typically have about 20 attack as it is, items that increase commander attack make almost no difference.
Troop attack/defence : is the main indicator of how much damage a unit will do on the battlefield as most commanders do relatively low damage in battles (and depending on field size, may not even get to fight). Troop attack for magic users has no effect unless you right click and select "Direct" to use direct attacks which is a melee attack that can only be used in the front row. This is generally a bad idea, except possibly for characters like Satella or Eleanor which have much better melee than magic stats.
Note that for some reason, ranged units such as Isoroku and Mill do massive damage to commanders despite having mediocre stats. They can easily clear multiple dragons at Rising Dragon Peak on her own whereas characters like Patton and Kaijuu Prince will struggle.
The difference of 1 attack or defence can make a lot of difference in calculating damage. Leazas soldiers (8 attack) vs monster melee units (7 defence) will only do about 10% of their strikes in damage. Increasing their attack by 1 allows them to do 5-10% more of their strikes in terms of damage up to a cap of about 90% of their strikes in damage. There is also a damage cap of approximately 600-700 regardless of stats or number of strikes.
Magic is how much damage the unit and it's commander (if a mage) will do when attacking/defending with magic. Satella for example, does very low damage due to her low magic level, even though she has pretty high commander stats. It also affects how much damage you take from magical attacks, if an enemy unit (such as Helman Knights) has high defence, attacking them with magic is a good way to deal more damage than with physical attacks.
Command abilities are bonuses to the troop attack/defence depending on whether the unit is attacking, defending or in a dungeon. Rick for example, is best used in offensive battles while Cordoba works best when defending.
Strategy chance is the odds of successfully implementing a strategy. This is typically +10 advantage, although sometimes you may get +50 advantage. Advantage affects how much damage you do and take from enemy attacks. For example if 10% of your strikes would cause damage,10 advantage would allow you to do 10% + 0.1 * 10% or 11% damage. If you had 50 advantage, you would do 10% + 0.5 * 10% or 15% damage. This makes strategy most effective when you have high stat troops, but most strategy commanders have Leazas soldiers with low stats. Strategy stacks with advantage from fighting in cities.
Everytime a commander levels, their strikes will increase by +1 and their command abilities may increase as well. This appears to be random, and you may not see a difference even after leveling a commander several times. This also means there is no real need to level most commanders as they won't improve much anyway (unless you are using the popularity staff).
Most skills fall into two categories, "snipe" skills like rance attacks which target a commander directly, and "bomb" skills that cause damage to the whole unit. Snipe skills do 1-4 damage and bomb skills do damage as if the attacking unit had the same size as the defending unit. Bomb skills also ignore field size limitations.
E.G. If Gandhi has 500 troops and uses his skill Evil Purging Overlord's Light vs a 3,000 strong unit, the damage is calculated as if Gandhi had 3,000 troops attacking. However there is a damage cap of approximately 600-700 damage. Because of this, bomb skills do no damage against solo units with no troops and can actually do less damage than normal attacks if the defender has a smaller unit size than the attacker.
Unless the field size is small or the target has high magic resistance, most bomb skills are also less efficient than attacking twice, assuming your unit size is approximately 400-500. Gandhi with 500 troops will usually deal more damage attacking twice than using his bomb skill against a unit with 0 magic resistance, assuming the field size allows him to use all his troops.