Considering the context that Jesus was engaged with the Pharisees and the subject that He alone was powerful enough to remove the Devil from his kingdom, various commentators seem to conclude that this is a parable to expose the true nature and hypocrisy of religion without Christ.
Religion pretends a higher morality than the common man and tries to show it by external boasts of ritualistic practices and avoidance of external common sins. Jesus says this is like a room that has been swept clean. However this, when without faith in Messiah is not filled with God, therefore all the better habitation of Satan in that he can live there without being noticed.
Some commentators explain the dry lands as the Gentiles, others as referring to Jewish legends about Devils, but this is not relevant to the main idea.
Naturally Christians apply this to the Jews. Some think it prophetical about the near future total depravity of Israel after rejecting her own Messiah. Others see this as historical in that after the Babylonian exile Israel has finally purged herself of idolatry which was considered the only Devil, yet this "sweeping" led to the greater wickedness of self-righteous pride and legalistic hypocrisy of the Pharisees.
I prefer the historical view as there is nothing in the verses directly indicating a future tense. This is the view taken by the Jewish Historian and Theologian Alfred Edersheim:
he came back ‘with seven other spirits more wicked than himself’—pride, self-righteousness, unbelief, and the like, the number seven being general—and thus the last state—Israel without the foulness of gross idolatry and garnished with all the adornments of Pharisaic devotion to the study and practice of the Law—was really worse than had been the first with all its open repulsiveness. (The Life and Times of Jesus the Messiah by Alfred Edersheim 2.201)
Therefore the action his disciples were to take is to ensure they do not just do a surface clean through vain religion but by faith receive Christ as the only "strong man" that alone can cast the kingdom of Satan from a heart. Otherwise, all one's religion and good works will be the perfect nest for every evil.