I assume the subject is geometry, and that "square" has its geometrical meaning. All three are acceptable, but in the second and third sentences it is better to change the phrase "the square" to "a square." To a modern ear, "the" refers to a particular square. If you say "each side of the square is the same length," you are saying that this is true of some particular square--but that other squares might have sides of different lengths. But every square has sides of the same length, so it is better to say "a square." Here's an example where "every side of the square is the same length" would be make sense. "When we were in Philadelphia, we visited the famous park, Rittenhouse Square. Every side of the square really is the same length. Most public 'squares' have sides of different length, but Rittenhouse Square really is a geometric square." Here, "the square" refers to one particular square--Rittenhouse Square.

This sentence sounds the most natural: Every side of a square is the same length.