He isn’t speaking of demonic possession. In my opinion, the devil cannot enter the heart of any overcoming Christian and claim a place in that person.
The figurative meaning of Paul’s word for stronghold in Greek is “holding firmly to an argument.” A stronghold is an accusation planted firmly in your mind. Satan establishes strongholds in the hearts of God’s people by planting falsehoods and misconceptions about God’s nature. For instance, the enemy may plant a lie in your mind that you’re unworthy of God’s grace. He may whisper to you repeatedly, “You’ll never be free of your besetting sin. You haven’t tried hard enough. God has lost patience with you because of your constant ups and downs.”
The devil may try to convince you that you have a right to bitterness and that God doesn’t mind your animosity. If you keep listening to his lies, you’ll begin to believe them. These lies can become Satan’s strongholds.
The only weapon that scares the devil is the same one that scared him in the wilderness temptations of Jesus. That weapon is the truth of the living Word of God. According to Micah, we are to cling to this promise: “Who is a God like you, pardoning iniquity and passing over the transgression of the remnant of his heritage? He does not retain his anger forever, because he delights in mercy. He will again have compassion on us, and will subdue our iniquities. You will cast all our sins into the depths of the sea” (Micah 7:18–19). We do not subdue our own sins. God will subdue them through repentance and faith.