The 64-year-old takes his first international camp in Manchester today and the Nigerian striker has told the squad that they can expect to be pushed hard in training.
Odemwingie, who bagged 10 goals for the Baggies last season, said that Hodgson is very demanding, but also very warm-hearted.
"He is a very intelligent and clever man and he is fair," The Mirror quotes Odemwingie as saying. "He demands 100% commitment, but for me that's only a plus, that he is a very demanding coach, even if at times he seems a bit harsh.
"In training he can be very tough, but once he blows the whistle to finish it, as soon as we start the walk back to the dressing rooms, he becomes a different person.
"He will walk with you, chatting, talk to you normally no matter what he's said out on the pitch, asking you about things that are happening in your life, turning it away from football to get to know you as a person and what makes you tick."
Odemwingie arrived at the Hawthorns from Lokomotiv Moscow in 2010.