One of my children was in the habit, as a child, of saying this: “I mean it.” When challenged a little more: “I really mean it.” And when a little more: “I really, really mean it.” Which means, when saying “I mean it” it was not fully meant. Jesus summoned those who wanted to follow him to be utterly honest.
Oaths, so Jesus was saying, are a form of making layers to truth-telling. If you make an oath, you are dead-serious about your words. Which leads to the genuine problem that sometimes what one is saying is not fully the truth. The swearing process — by heaven, by earth, or by Jerusalem — is over for those who follow Jesus. So, evidently, Jesus seems to be saying.

Not all agree. Some think Jesus is only eliminating oaths in earthy, normal discourse. Others would say it is OK to use oaths in public courtrooms and the like — after all, it is the way the court knows you really, really mean it — while others would argue that this is just the only way we can get along in this fallen world.
The Anabaptists called the Church to listen a little longer to what Jesus was saying and said that oaths were not needed for those who always told the truth. If you mean “yes” say “yes” and if you mean “no” say “no.” Mixing yesses with nos confuses human relations. Telling the truth keeps things above ground.
For my part, Jesus is summoning his followers to the will of God for kingdom life; honesty is the practice so that oaths will not be needed. And, I would also contend that just as Jesus “overdoes” it a bit with divorce and adultery and murder, so he over does it a bit with telling the truth.
The point he is making is pretty clear: tell the truth and you will not be in need of a world filled with layers of truth telling. I think that instead of wondering if it is OK to use an oath in court we ought to wonder why we need oaths at all. In a world filled with salespersons who shade the story so they can gain a buck, we need to respond to the summons of Jesus to follow him by becoming honest, truth-telling followers.