Odemwingie earned himself a new, three-year, £40,000-a-week contract last season, grabbing 15 goals following his move from Lokomotiv Moscow.
But the 30-year-old Nigerian has struck just twice in nine games this season and has been struggling with a knee injury. And Hodgson has questioned Odemwingie's desire to play for West Brom, having seen the player abort several scheduled comebacks.
He said: 'I'm frustrated because we've got nothing out of him this year. 'He didn't take part in many of the pre-season matches and he hasn't taken part in many of the matches since then. 'It's been one problem after another.'
Hodgson added: 'Peter is difficult to work out - you would have to speak to the doctor about him. 'This is still the same problem he's had for a month. He was supposed to be fit for the Arsenal game but wasn't. 'Then he was definitely going to be fit for the Bolton game but wasn't. 'And he is supposed to be fit for the Tottenham game and now there's a doubt about that too.
'So I take any optimism with a pinch of salt.' Hodgson said that the Baggies have not had value for money on the new deal dished out to Odemwingie, and compared the striker unfavourably to players he says are battling to play despite fitness issues.
Hodgson complained: 'For a player who we really put so much into in the hope that he would be a major force for staying in the Premier League we have not had much of a return.
'What makes it even harder is when you get a player who is frustrated or is frustrating it gets highlighted more when you have players like the (Zoltan) Geras, (Shane) Longs, (Steven) Reids and the (Jerome) Thomas's who play through pain every week.'
The former Liverpool and Fulham boss also said that fellow striker Long's arrival for £4.5m from Reading in the summer does not excuse Odemwingie for missing games.
He added: 'When you sign that contract and accept a lot more money following a good season, then you automatically accept that the club thinks you're the man and that can put pressure on you.
'Your star players need to be available for selection - the fact someone else might have come in and done well is irrelevant. 'There is a hierarchy at every football club.'