“If a just, merciful, omnipotent God existed and loved all mankind, it is difficult to fathom why such a loving Creator would not only allow these disasters to occur and kill innocent nonbelievers and believers alike, but actually cause them.” We need to look at his definitions of the words "just", "merciful", and "omnipotent".
First, I believe that natural disasters are a result of free-will. Some Christians may disagree with me but they have the freedom to be wrong if they want ;-). I believe when Adam/Eve sinned it plunged the universe into a state of decay. Romans 8:20-22 says, "For the creation was subjected to futility, not willingly, but because of Him who subjected it, in hope that the creation itself also will be set free from its slavery to corruption into the freedom of the glory of the children of God. For we know that the whole creation groans and suffers the pains of childbirth together until now." Notice that the creation was not created in a state of futility but was subjected to it. This futility is a "slavery to corruption". It seems then that thorns and thistles (Gen 3:17-19) was not part of God's original plan. Therefore, I believe that natural disasters are a result of man's free-will choice to reject God. The Lord, because of our sin, would not allow us to live in a garden paradise but subjected us to a creation that is in the process of decaying.
Second, I would ask, "Is God always the ultimate cause?" Aristotle distinguished Four Causes; Material, Sufficient, Formal, Final. To study that a bit more click here. But let me give you an illustration to show there is not always one cause. Two sets of parents both had kids. Set A actively taught their kid how to steal but Set B taught there kid how to work for a living. But both kids grow up to be thieves. Are both Set A and Set B parents responsible in the same way? Absolutely not!!! Set A could be charged alongside their child but Set B wouldn't be ultimately responsible. We could only charge Set B with the cause of creating the child to begin with but that is not their fault if he becomes a thief in direct opposition to their training. God is like the parents of Set B. We can only charge Him with creating a world that gives rise to the possibility of natural disasters but we can not charge his directly for those natural disasters. We are the sinners and we are responsible for having this world subjected to futility.
Third, God could be just and kill everyone through natural disasters. Even if we conceded that God was the ultimate cause of every natural disaster it wouldn't make him unjust. We are sinners and all deserve to be in Hell today. God is so loving and patient that He held off his wrath in order to work out a scheme of redemption for us!!! So yes David, God could be just and kill us all. So you should praise him for giving you another day to disregard His mercies.
Fourth, David's definition of "merciful" would lead to a place we call heaven. The implied idea in his question is that a merciful God wouldn't allow any bad things to happen to us. That is, we would live in a world without any moral or natural evil. Ummmm....yea...about that.....Hey David we call that place Heaven. You see that is the whole story of the Bible. God planted mankind in a paradise without moral or natural evil, we screwed it up, and God is in the process of fixing it. He has established a plan by which you can escape this universe corrupted by evil and live with him for an eternity. So David are you ready to put your trust in Christ as savior?
Fifth, just because God hasn't done something doesn't mean He can't do it. David's definition of "omnipotence" is simply a regurgitation Epicurus' contention:
“Is God willing to prevent evil, but not able? Then he is not omnipotent.
Is he able, but not willing? Then he is malevolent.
Is he both able and willing? Then whence cometh evil?
Is he neither able nor willing? Then why call him God?”
The answer is that God is both willing and able. Just because He hasn't finalized His plan doesn't mean He isn't willing or able. For example God has already condemned sin when Jesus died on the cross (Rom 8:3). And God has already told us He will judge the world casting both sin and unrepentant sinners into the lake of fire (Rev 20:10-15). Therefore, David has a false definition of "omnipotence".
Sixth, we don't have the perspective to say whether a natural disaster actually is for our good. At first glance this may seem shocking but stop to think about it. I have been to Louisiana 5 times to help out with Katrina Relief. For all my time down there the greatest memory I have is the Church getting out into the community to spread the Gospel in the aftermath by showing their love for the people. I saw many people come to faith in Christ due to this. Think of all the souls who would not be going to heaven if it wasn't for Katrina. Some will say, why couldn't God find another way to convert them?!?! I would contend, maybe He tried but they were unwilling and He had to shock them in order to get their attention. I trust God's hand of control because I trust His heart to save sinners.
Natural disasters are not outside the control of God. They are a result of a fallen creation do to our sin. But God can use them for His good. That is not to mean He is always the direct cause of them but no matter what God is in control. Natural disasters do not contradict God's justice, love, mercy, or power.