Why do God and Jesus seem so different? God destroyed the world with a flood, destroyed all the people in Sodom and Gomorrah, gruesome sacrifices, laws for stoning people, Jericho, requesting the sacrifice of Abraham's son, the sacrifice of God's own son Jesus'. Jesus seems so different to me because instead of making life or taking life he gave his own, he preached forgiveness and grace and seemed to defy the laws made in Leviticus. I'm a christian but I am having a hard time understanding this, especially if one believes the Trinity doctrine.
If you look at the role of Jesus especially at the very end of time and the beginning of eternity (eternity for us, that is to say) he does not seem that different after all. When Jesus returns, he will not return as the contemporary hippie Jesus. That image is a product of modern humanistic culture and not the Jesus of scriptures. He will return as the King of kings, terrifying in his righteous wrath. That will be a day of devastation for anybody who does not want anything to do with him.

One striking difference between Noah and the flood vs Abraham and Sodom/Gomorrah is that Abraham was the one who thought that perhaps there was still hope for the two cities. Noah did not. Abraham pleaded with God and God agreed upon a minimum number of righteous people who, if present, would be grounds for not carrying out the punishment. A similar incident happened during the early exodus, when God, appalled at the golden calf the Israelites had made, offered Moses to destroy them all and make him the new god's people. Moses turned the offer down.

It is almost as if God tries to provoke a reaction. If Moses' reaction had been "yes, let's do away with them wrongdoers" God most certainly would have carried out his threat, as his righteousness demands. God never bluffs. At the same time He would have been disappointed in the hard-heartedness of Moses.

I believe this type of thinking can be applied to the mosaic law. It gives a human being an apparent right to stone another, but it does not take away the possibility to show compassion. The problem is that the israelites rarely did that. It tells more about man than it tells about God. The tendency to point fingers at each other and not see our own error is a product of the god-syndrome mankind fell victim of in the garden of Eden. That is something Jesus pointed out, and that is just what he did; he did not introduce a new hippie religion or change, defy, or undo the law, but pointed out how the law should have been applied in the first place. He explained what the law really is and is supposed to be; a dilemma.

I hope this answer helps and manages to touch all the different issues in your question.