Can extras player (more than 11) in a team can play the role of a runner for a team player who is injured in a cricket test, odi or t20 game in terms of laws and rules?
No. Law 25 Players, substitutes, runners and practice is very clear on this:
25.5.2 A runner shall be a member of the batting side.
This could of course be overridden by the playing conditions for any particular tournament, but I don't believe it is for any ICC matches.