Yes, insects have muscles, which they use to move their legs and other body parts. However, since their skeleton is external instead of internal like ours, the mechanics are a bit different as the muscle bundles are attached to the inside of the exoskeleton. Also, their muscles are not red like ours because they don't have the same pigments.
And they also have fat, which usually accumulates in so-called "fat body", located mainly in the insect's abdomen. The fat body is very important to supply energy and regulate metabolism.
As for their strength: analogies such as the one you mention (A would be able to do X if they were the size of B) are tricky - because of some basic biomechanical laws, greater size does not automatically mean greater strength; in fact, insects as large as humans would never have the same shape that their small counterparts have, and would have lots of trouble to even support themselves without even trying to lift cars!
That being said, ants are able to lift stuff that is very heavy compared to their own weight, so yes, they're relatively very strong.
EDIT: Oh, I see what you mean. Yes it's common knowledge to me, but then again I'm a zoologist :-)
There will always be individual differences: some ants will be a bit larger and others a bit smaller, so that could help them be stronger. However, since the muscles of ants are on the inside of their skeleton, you wouldn't see a mini-Schwarzenegger ant (btw have you seen "Antz" the movie? nothing like that). The variation could also be undetectable from the outside, for example, two ants could look the same externally, but their muscles or muscle attachment sites inside could be different so that one is stronger than the other (different lever arms for the muscles).
Also, in a single ant colony (the same for bees, termites and other true social insects) there are different types of individuals. The "soldiers" in charge of defense sometimes have a big head with strong jaws, or special glands, etc; but also the "workers" are very strong because they're the ones that carry the food.
I hope this makes it clearer :-)