While Jesus spread the good news of salvation and primarily taught New Testament (NT) with his disciples (He did not primarily teach or promote OT or the Old Testament); The NT did not officially begin until Christ's death. It's why the Temple veil was torn (Letting us know the sacrificial system involving the Levitical priesthood was no more). In fact, Jesus was changing things, even within His ministry. He said to no longer render an eye for an eye (Which is OT) but instead he said for us to turn the other cheek (Which is an NT teaching). Peter was told by God in a vision that he could now eat unclean animals. If the OT Law was still binding, then Peter would be breaking the OT Law. In the OT, God had blessed Solomon with great material wealth. But in the NT, he told the rich young ruler that he needed to sell that he had in order to be perfect. This is a change between the OT and the NT. It's why Jesus said no man puts new wine into old wine skins.
The Commands that John talks about in obeying the Lord in his epistles (After Christ's death and resurrection) is in reference to the two greatest commands the Lord had mentioned in the New Testament (Which is taken from the Old but clarified in the New). This is to love God and to love your neighbor. Loving your neighbor fulfills the Law according to Paul (See Romans 13). The Commands are in reference to preaching the gospel and in helping those who are poor, etc. This again, is based on the law of Love or the Law of Christ. We love people when we care about their spriitual and physical well being. In other words, if I took an apple seed and smashed it with a hammer, I would be destroying the Law. But if I let that apple seed be planted in the ground properly, it can then be fulfilled into it's intended purpose or function as an apple tree (i.e. the Law is fulfilled in Jesus Christ).
