Odegaard's double puts him up to six Premier League goals this season, the most of any Arsenal player, while only Kevin de Bruyne, James Maddison and Leandro Trossard have been involved in more away goals than the Norway international (five, four goals and one assist).
The three points, combined with City slipping up, gives Arsenal their biggest lead at the top of the Premier League since December 2013.
Mikel Arteta's men are the only team to have scored in every Premier League game this season and they will be top of the league on Christmas day for the first time since the 2007-08 campaign.
Another defeat for Wolves means new boss Julen Lopetegui has much work to do, with the Molineux club bottom at Christmas for the first time since the 2003-04 season.
They are seriously out of form, only winning one of their last 22 Premier League games, failing to score in 11 matches over that run.