Generational curses are those judgements which pass down through the generations due to continued disobedience of those upon whom the curse is pronounced and those and their children who continue in that disobedience. The Judgement is lifted when there is a departure from the disobedience and a return to God.
The curse of the law was the approach to the law taken by the Jews. That is to say, they felt that if they could keep the law perfectly, then God would "owe" them salvation. The curse came because nobody could do it. The curse was lifted and the law fulfilled when Jesus kept the "works of the law" perfectly. See Galatians chapter 3 and Romans chapter 7 for Paul's discussion of this important principle.
I hope you have found this helpful.