By virtue of a win over Team WCW and Team Piper at Uncensored 1997, the nWo has the right to challenge for any WCW title at any time.
Strictly speaking, that means they could challenge for the World Title (containing the WCW World Title), the I-C Title (containing the WCW U.S. Title) and the Tag Team Title (containing the WCW Tag Team Title) in the WWF. But of those titles, only WCW's Big Gold Belt remains on TV.
So theoretically speaking, we could expect any of those men to get a shot at the World Heavyweight Title at any time, because they can challenge for any WCW title.
Not that Vince (nor anybody else but me and the guys at DDT Digest) would remember that, though.
John Cena is NOT the next level down from those men, and he is NOT on a level with Edge and Matt Hardy. He is a third-tier wrestler at best. He may be great some day, but right now he's green as hell and pretty sloppy also.