The concept of omnipotence is severely misunderstood by both unbelievers and Christians alike. With a correct understanding of omnipotence, several atheistic arguments dissipate, from foolish arguments like "can God create a round square?" to more sophisticated arguments, like the problem of evil.
Omnipotence, contrary to popular belief, is not the ability to do literally anything, even if it is meaningless and illogical. In fact, the irony is, if you were to grant that omnipotence does mean the ability to even create a contradiction, you have allowed the objection to answer the question. Can God make a box He can't look into? Yes, but He can still look into the box. The answer doesn't make sense, but neither does the question.
A correct understanding of omnipotence is that God is sovereign over His creation. All things that are not God are under God's control. If God wants to give a child to a 90 year old barren woman, He can give a child to a 90 year old barren woman. If God wants to split a sea in half so the Israelites could cross it, He can split a sea so the Israelites can cross it. If God wants a virgin to give birth, if God wants water to be wine, if God wants a man to walk on water, even if God wants a dead man to walk right out of His tomb, He is more than capable of bringing all these things to pass. But there are several things God can't do.
Interestingly, the Bible explicitly says there are things God cannot do. Titus 1:2, for example, says God cannot lie. What's ironic here is that lying, of course, is entirely possible. Man can lie. Satan and his forces can lie. Yet, God cannot. Why? Because it is simply not a Godly thing to do.
You can think about it this way. There are many things we have the physical ability to do, yet to do so is not in our nature. Physically, it is very easy to kill a baby. Newborns even have two soft spots, allowing easy access to the brain with a sharp object. Now, for me, even typing that very sentence, and proofreading it, makes me very sick. Though I am not yet a father myself, every instinct within me tells me that a child must be protected. Thus, I can legitimately say "I cannot kill a child" because although it would be very physically easy to do, it is repugnant to me to even think about killing a child in a hypothetical sense. Thus, I cannot do it.
Similarly, lying is not in God's nature. Sin of all kind is repugnant to God, so much so that He actually declares death as the sentence. Thus, God cannot lie. With regard to logic, a round square is also not in God's nature. It is illogical, and God is not an illogical being. It is confusing, and God is not the author of confusion. Thus, just because of the very nature of God, a round square falls under things that are impossible even for God. However, all things that are possible are possible for God because of His power.
Another thing that falls within God's power is the salvation of sinners. Though sin is against His nature, so also is callousness. In His unfathomable love, though God cannot tolerate sin, He has provided a way of reconciliation through the Man Jesus Christ. As God in flesh, Jesus suffered the wrath owed to man for our sin. The punishment has already been dealt. Therefore, God no longer needs to punish man. However, this gift must be received. It is essential to confess Jesus as Lord and believe He rose from the dead. Failing this will result in eternal punishment. But if you believe, you will inherit eternal life in a Kingdom completely sustained by the Lord.