Does Satan still have 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:

Genesis Lesson 41B

Exodus Lesson 24

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:

Rev. 20:10 And  the devil who  deceived them was thrown into the  lake of fire and  brimstone, where the  beast and the  false prophet are also; and they will be  tormented day and night forever and ever.