While I wouldn't claim to support everything every pastor says (I'm quite sure I don't) I would point out a few things about the old testament. First, not all of it is the literal word of God or even claims to be. Second, Jesus broke the old covenant and created a new one. This did in fact negate at least some of the Old Testament. Third, there are plenty of things in the Old Testament that virtually no Christians follow today: certain eating habits, certain clothing habits, certain punishments for certain crimes or sins, etc.
The New Testament is why Christians are different than Jews and why we don't follow all the same rules. The Old Testament certainly shouldn't be ignored but what applies to modern Christians and what doesn't as well as the context can be a complicated subject and it's really one that isn't discussed enough I think. When these rules are reiterated, modified or mentioned in some other way in the New Testament then it is easy. When they aren't, interpretation is going to vary. In either case, the Old Testament is important context for interpreting the New Testament.