Can Satan perform miracles and if so by what and whose power? I thought the Bible teaches that Jesus stripped him of all his power?
Satan can perform "miracles" in the sense that he has power to manifest supernatural wonders and signs. The power of the enemy is often called the "dark arts" or sorcery. We find examples of it in many places in both the Old and New Testaments:
Ex. 7:8 Now the LORD spoke to Moses and Aaron, saying,
Ex. 7:9 “When Pharaoh speaks to you, saying, ‘ Work a miracle,’ then you shall say to Aaron, ‘ Take your staff and throw it down before Pharaoh, that it may become a serpent.’”
Ex. 7:10 So Moses and Aaron came to Pharaoh, and thus they did just as the LORD had commanded; and Aaron threw his staff down before Pharaoh and his servants, and it became a serpent.
Ex. 7:11 Then Pharaoh also called for the wise men and the sorcerers, and they also, the magicians of Egypt, did the same with their secret arts.
Ex. 7:12 For each one threw down his staff and they turned into serpents. But Aaron’s staff swallowed up their staffs.
Mark 13:21 “And then if anyone says to you, ‘Behold, here is the Christ’; or, ‘Behold, He is there’; do not believe him;
Mark 13:22 for false Christs and false prophets will arise, and will show signs and wonders, in order to lead astray, if possible, the elect.
Mark 13:23 “But take heed; behold, I have told you everything in advance.
Notice how in the past the demonic realm commanded power over physical elements, though their power was not greater than the power of God. Also notice that Jesus taught that in the future we should expect to see the demonic realm performing great miracles and signs, which will lead astray many. This is further evidence that the demonic realm still has power to perform miracles.
You can learn more about Satan's power to perform miracles by listening to the following lessons from our Exodus and Genesis studies:
You commented that "Jesus stripped Satan of his power," but that statement isn't an accurate summary of what the Bible teaches. Specifically, the Bible says:
Heb. 2:14 Therefore, since the children share in flesh and blood, He Himself likewise also partook of the same, that through death He might render powerless him who had the power of death, that is, the devil,
Heb. 2:15 and might free those who through fear of death were subject to slavery all their lives.
The Bible says that Christ's work of redemption by His death rendered Satan powerless over our death. As Christians, we no longer have reason to fear death. Jesus rendered Satan powerless to condemn us and to enslave us by our fear of death and judgment. On the other hand, the Bible does NOT say that Jesus eliminated Satan's power.
On the contrary, the Bible warns believers not to underestimate Satan's power to ensnare us:
1Tim. 3:4 [An elder] must be one who manages his own household well, keeping his children under control with all dignity
1Tim. 3:5 (but if a man does not know how to manage his own household, how will he take care of the church of God?),
1Tim. 3:6 and not a new convert, so that he will not become conceited and fall into the condemnation incurred by the devil.
1Tim. 3:7 And he must have a good reputation with those outside the church, so that he will not fall into reproach and the snare of the devil.
1Pet. 5:8 Be of sober spirit, be on the alert. Your adversary, the devil, prowls around like a roaring lion, seeking someone to devour.
1Pet. 5:9 But resist him, firm in your faith, knowing that the same experiences of suffering are being accomplished by your brethren who are in the world.
Eph. 6:11 Put on the full armor of God, so that you will be able to stand firm against the schemes of the devil.
Eph. 6:12 For our struggle is not against flesh and blood, but against the rulers, against the powers, against the world forces of this darkness, against the spiritual forces of wickedness in the heavenly places.
Eph. 6:13 Therefore, take up the full armor of God, so that you will be able to resist in the evil day, and having done everything, to stand firm.
The Bible repeated instructs believers not to underestimate the power of the enemy nor discount the craftiness of his schemes. In fact, even angels show consideration for the power of the enemy:
Jude 8 Yet in the same way these men, also by dreaming, defile the flesh, and reject authority, and revile angelic majesties.
Jude 9 But Michael the archangel, when he disputed with the devil and argued about the body of Moses, did not dare pronounce against him a railing judgment, but said, “ The Lord rebuke you!”
Clearly, the enemy has power that even the archangel Michael respected. He declared that the Lord would rebuke the devil. So we have good reason to give the enemy his due, even as we understand that the Lord has taken away the enemy's power over our death. Therefore, we may acknowledge the enemy's power and remain diligent against his schemes, while having no fear of him and remaining confident in the Lord's eventual triumph.'
One day the Lord will destroy the enemy: