As much shock value as the evil God argument has, the fact is, it is so entirely worthless, it can be summed up as "I don't like God, therefore He doesn't exist".
See, if there is no God, morality is just an opinion. You might think of it as being like a law. The only way for a thing to become illegal is if an authoritative body declares it so. Take, for example, the side of the road on which we drive. Here in England, we drive on the left side of the road, whereas in America, they drive on the right. It should be obvious that neither side here is objectively right, but it can be said that in whichever country you are, you are legally required to drive on the correct side of the road.
There are two things to note here. The first is that even the law technically has no objective grounding in reality. It's just the way in which a specific organisation has decided everyone else must behave, and how they will likely react to those who don't. But there is no world in which might = right. Thus, if there is no God, even the law is devoid of legitimate authority.
But the second thing to note is the distinction between the law I chose as an example and other laws which are obviously objective. Any government can say "you must drive on the left" or "you must drive on the right", and no matter which law they make, they can't really be judged for it. But you're a truly despicable person if you think any government anywhere on earth should be allowed to legalise murder. You instinctively recognise the difference between moral laws and driving laws.
This is because there is a difference. There is an authority higher than any human institution that dictates moral laws, and whether you want to acknowledge it or not, you know it. And so the question is, what, or more accurately who is it?
However you answer that question, you must acknowledge that it is not you. If you want to claim any authority at all, you must answer one question: Where did you get it? For God, the answer is simple. There was God when nothing else existed. As God asks Job, "who has preceded me, that I should pay him?" Everything, be it a thing to have authority over, or a being/institution to have authority over it, owes its very existence to God. Even your own body is a product of the God who gave it to you.
And so there are two major fallacies in claiming God is evil. The first is that you are saying that's not true, and yet this is the very point you are trying to prove. You cannot use your assumption that God does not exist in an attempt to prove God does not exist. If God exists, God cannot be evil, and so by saying God is evil, you are saying "God does not exist, therefore God does not exist."
But the second fallacy is that you are using authority that you do not have in a foolish attempt to overrule the authority God does have. This is called sin. Foolish person, you are the defendant attempting to convict the judge! Will this folly succeed? Of course not! You have no gun capable of killing God, no prison capable of containing Him, no hand cuffs capable of restraining Him, and no authority capable of overruling Him. Your sin is fatal.
But maybe not for you. See, you have every right to go on sinning until the day you die, at which point the Lord will repay you for every evil deed, every idle word, and every unholy thought. The alternative, however, is to "lawyer up". See, God, whose authority is matched by His great love, does not desire to punish you. Rather, even before you took your first breath, He put a plan into action to grant you eternal life. Rather than punishing you, God sent Jesus to live as a man, die on a cross, and rise again. Jesus never sinned, yet was punished as if He did. Therefore, you, who have sinned, can be rewarded as if you never did. The choice is yours. Puff yourself up and fall, or swallow your pride and be saved. Choose wisely.