Strength is your damage modifier. The general formula for damage modifications is Base*(Strength/500). However, there are exceptions that will be covered later in this post.
One example: Just because Shawn has higher strength than Gordon does not mean he does more damage. Gordon's base damage is much higher, so the lower strength multiplier still makes him do more damage than Shawn's bow attack.
Clickies: Gordon vs Shawn

However, if the levels between two fighters are not even, the damage will be altered. I do not know how much the damage is multiplied between the differences between levels, but it is pretty steep from just three or four levels.
Clickies: Higher than vs Lower than

UPDATE:
Normalized, your strength is 500. Your attacks will only deal the base amount (which is pretty much how HF was before the level system). Even though you gain a lot more strength in the higher levels, it starts covering the higher amounts of health in these levels. There is a modifier in place to lower damage in case the damage is too much. While beneficial for higher levels to not be as damaging, lower levels still have to face a steep penalty. In Hero Fighter X, there are limiters present to ensure damage wouldn't be too high or too low.

The breakdown of how strength works is extremely complicated. First of all, the HP values displayed on the character list do NOT reflect the actual HP values, and follow the same growth formula as Strength itself. As for Strength itself, the list is accurate to real values. The formula for strength growth and modification is in the code here. My initial theory of levels modifying strength is only the case in HFX. In the PC version, a character's strength is modified in case there is a big enough gap between the two characters' strength values. The damage is slightly lowered if you have twice the strength of your opponent, but the damage takes another HUGE drop if your strength after the first cut is three times greater than your opponent's. This is a little hard to imagine, but this countermeasure only exists to balance out how much damage you'll do to your opponent when they're at an extremely low level. It's still a relatively hefty amount for them to take. Your damage is still lowered if you have less than half of your opponent's strength, which is slightly steeper than having more strength than your opponent.

Honestly though, Marti should have never added in the drastic modifier between levels as that is what ruined story mode. The math he did was impressive, but a lot of numbers going on behind the scenes messes with the player's intuition. There surely had to be a better solution. Anyway, the list of damage for each attack is listed in the other thread.

In LF2, characters had 40 points of guard. Moving around made it easier for them to be broken. In this game I'm going to use LF2's system as a reference. A general rule of thumb is that a basic four hit combo broke a guard standing while the first three hits would break guards if they were moving. Walking with a guard reduces your limit by 5 points, and running reduces it by 10. I'll figure out a way to cover this in proper detail later. You can look at my doc in the other thread in the meantime. 

Coming Soon. Someone has mostly covered this part already, but I'm waiting to cover more important notes.

Tuning: Hit Stun deterioration (damage and stun will be reduced in high combos, prevent sudden kill in seconds)
This is a very complicated explanation for a common game mechanic in fighting games known as damage scaling. The more hits you do in a combo, the less each hit does. There are also fighting games that lower the time you stay hurt the longer the combo Hero Fighter has a limit.  It turns out damage deteriorates at Nirvana's lucky number 150 for most characters (170 for characters like Drew and Gordon). If an attack were to make a combo go over that number, the damage starts to become less. The next hit will do 1/4 damage, and the rest will do 1/10 damage. Keep in mind that it is only possible to do up to 12 hits on the floor, and 10 hits with a juggle; Gordon and Drew have one less hit in both situations. One final thing to note is that combos are counted not on the player, but on the victim, so two people attacking one person would count as one combo.

Here's an example of Livermore's damages from his Hurricane Kick: 45, 45, 45, 23, 11, 5, 5, 5, 5, 5
For a simpler example, here's when Titto spams his attack: 30, 30, 30, 30, 30, 15, 7, 3, 3, 3, 3, 3

Another example with Lucas using the same moves in a different order:
AAAA, Uppercut= 30, 30, 30, 45, 30(60) = 165
Uppercut, AAAA= 60, 30, 30, 30, 22(45) = 172
As stated earlier, any hit that causes the damage to go over 150 is affected by the scaling, so following up with an uppercut after the last hit causes less damage overall.

Damage is reset whenever the opponent flips or gets up. In crazy mode, simply getting up yields no invulnerability for whatever reason, so rolling is always the safest option to go unless your opponent is close enough for you to handspring which also leaves no invulnerability. As for flipping, it creates a risk for followups so careless flipping is punished unlike pre-0.6 where flipping was always the best option because you would take full damage regardless.

Information to be added: How combos can be elongated, more examples

Everyone has 500 SP, and uses a double variable (which means it can support a decimal value). The max SP is used in calculation with an exponential function to multiply itself to recover more over time. Obviously, the time exponent resets whenever you do something that drains SP. I believe it was originally 2 SP per frame, and now it's 2.5 which adds up with an exponent based on how long you've been .
Until the exact numbers can be figured out, pre-0.5a's stamina recovery took 250 frames and now it takes 90 (three seconds) frames from 0 to 500 as of 0.70. 

st = st + (2.5 + this.st_s * this.st_s / 800);
this.st_s++;

As far as Stamina consumption goes, costs for each action were all generally the same across the cast until 0.5a; the only exception was when you had a giant object. What seemed like characters having high and low amounts of stamina was actually the costs of SP being altered. The intent was to fix the problem of running away, but the numbers pushed mobility to extremes. In fact, Gordon and Titto have the same consumption despite Titto having lower mobility.

Coming Soon