an authoritative directive: a binding order from someone with the right to give it
At its core this word names a single instruction that carries authority. Someone who has the standing to be obeyed tells someone else what to do, and that order is an ἐντολή. The weight of the word comes from who is speaking, not from the topic.
Most of the time in the New Testament the one giving the order is God, so the word most often points to a precept of the law given through Moses, whether a single command (like the command not to covet that Paul wrestles with) or the whole body of God's commands taken together. But the same word covers any binding charge: an official's edict, the chief priests' order to report where Jesus was, a parting instruction Paul leaves with a companion.
In John's writings and the letters of John the word takes on a sharper point. Jesus gives his followers commandments, and above all a single new command to love one another. Here the obligation is no longer the written code but the will of Jesus himself, kept out of love rather than mere duty.
The senses below are not different words; they are the same idea of a binding directive seen against different backgrounds: the law of Moses, an ordinary human charge, and the command of Jesus.