The huge difference between the strong and the electromagnetic force consists of their range. As you said, the strong force has an extremely short range. In contrast, the EM force as an infinite range (although it is mainly screened). This is why we can do things with EM, whilst we can do anything with the strong force without breaking the atoms first.
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And that freaks me out a little. How can a force (the strong force) overcome the electromagnetic force binding same charge protons in a nucleus, but its field only extends a short distance? That's weird. It's super powerful, yet super limited. But I have the same trouble understanding gravity, which seems to be a puny little force (it takes so much freaking mass to create it, it's ridiculous). Yet its range seems infinite.
The strong force has a range of a bunch of femtometers. This is the order of magnitude of the atomic nucleus. Therefore, strong interactions are relevant here.
Gravity is the weakest of all forces. On top of that, it is proportional to the masses of the interacting objects, which makes it even weaker. Why it is so weak is a good question. The good answer is probably that we don't know (at least yet :) ).
With the crazy stuff in 11-dimensional string theory, anything is possible. There could be a spatial dimension orthogonal to the ones we know about, but is inaccessible (for some reason) to us mere 3 dimensional beings. Occasionally, we see things popping in and out of our 3D hyperplane that we can't explain (like particles in the Dirac sea?), so why can't forces dissipate out of our hyperplane into surrounding ones? That might explain the weakness of gravity, if it were a force that we are "sharing" with other multidimensions.