I think most native English speakers would consider these words to have the same meaning. However, "quarrel" may have the nuance of a small disagreement with someone you normally are friendly with. You may quarrel with your siblings for example. "Dispute" may mean a disagreement over an issue that may involve more formal arguments. Countries may have disputes over land for example. "Altercation", to me, implies a more angry argument. In casual speech, however, I think they can all be used in the same way.