The Midlands side are 15th in the Premier League table, six points above the relegation zone.
"There will be pressure for all the clubs in the bottom of the table," The Mirror quotes Odemwingie as saying. "In a way it's exciting, but I only hope we can get all the points necessary to avoid having a very nervous end to the season.
"Bolton and Blackburn both won away recently, so I think it's going to get tough now and every point will be very important."
The Baggies host Norwich City at the Hawthorns on the back of four defeats in their last six home fixtures.