You have 1998 series New twenty dollar bills with a 1996 misprint are they worth saving?

Only if you're afraid to spend them. Bills are dated by "series" and not by the year they were printed. A series currently begins when a new Treasury Secretary takes office and ends when they leave. In the past, series were even longer - the 1935 $1 bill series was printed until the mid-1960s, for example!