Strenght does increase the force of impact and damage done, yes. I don't recall the exact equation, but putting more mass/raw strenght behind a strike increases the impact in direct proportion, while increasing velocity of a strike increases impact energy in a logarithmic (?) proportion.

So if mass of strike is doubled while velocity remains same, the energy is doubled. If velocity is doubled while mass remains the same, the impact energy is tripled.

Human body produces strenght in several way. When it comes to striking with weapons, we're mostly in the realm of plyometrics and explosive strenght - trying to extert as much force as possible, as fast as possible. Even a relatively small and thin person can accelerate a light weapon (such as a knife) into dangerous speeds, but after a point (or if switching to a heavier weapon) they're going to need more muscle mass to accelerate it faster, which also puts more weight and raw strenght behind the blow.

Now, you don't need all that much force to cause lethal injuries to a human with a weapon, especially if it's bladed or piercing. Rather the difference becomes sever "important arteries vs. sever a whole limb" or "cause lethal concussion vs. cave a man's skull in". Things change if the target is wearing some sort of armor - something tougher than human flesh, as you put it. If you're fighting someone in padded armor with a Bo stick, your stick has to move much quicker and with much greater force to inflict the same level of injuries. Likewise, a steel spike or a warhammer can pierce through steel armor, but it's not something achievable with a light tap.