Cameron and Odemwingie only joined up with the squad this week having being granted extended leave after they helped their countries, USA and Nigeria respectively, reach the knockout stages of the World Cup in Brazil last month.
Cameron, handed the captaincy, started in his preferred central defensive role, while Odemwingie took his place in attack in a side containing a mixture of fringe players, new signings and youngsters.
There were chances at both ends throughout the afternoon and Albion competed well against their Premier League visitors, with summer signing Lucas Akins standing out for last season's Sky Bet League Two play-off finalists.
Akins saw a shot strike a post after 15 minutes when he cut inside from the right-hand side. The former Stevenage forward then worked Stoke goalkeeper Jack Butland twice in as many minutes midway through the first half, forcing the England goalkeeper to tip the ball away for a corner before making him produce a brave point-blank save.
Stoke might have stolen the lead when Steve Sidwell had the ball in the net in the 44th minute, but his effort was ruled out for offside. Albion goalkeeper Jon McLaughlin then did well to repel a Geoff Cameron header.
Akins continued to torment the Potters in the second half, and Butland had to get down quickly to parry another shot.
Substitute James Alabi headed against the crossbar on the hour mark for Stoke, who could have won it right at the end but Ian Sharps blocked Ollie Shelton's goalbound volley.
Stoke continue their preparations for the new season on Sunday when a much stronger side is set to take on Blackburn Rovers at Ewood Park.
Stoke XI: Butland; Shotton, Cameron (Watkins 46), Teixeira, Wheeler; Odemwingie (Alabi 46), Palacios (Shenton 59), Sidwell, Ness, Shea; Jerome