Odemwingie was given time off over the weekend and missed Sunday's 1-0 home defeat to Tottenham, the Baggies fifth loss in their last six Barclays Premier League matches.
The 31-year-old is expected to return to training at some stage this week after driving to Loftus Road without permission on transfer deadline day in the hope a move to QPR would go through.
That followed a series of Twitter rants against the club after a transfer request was rejected.
But when asked how the situation had affected the dressing room, Reid said: "Not a great deal to be honest. We've got a strong group with a lot of leaders in the dressing room who have good, strong characters.
"It's a matter that the club are dealing with now and I'm not sure what the outcome will be. It's up to them how they deal with that.
"There's enough characters and leaders in the dressing room to get through it.
"Maybe that group wasn't as strong when I first joined but it is now and maybe that's why we're in the position we are in in the league.
"It (Odemwingie's behaviour) is not the way I'd go about doing things and I'm sure it's not the way a lot of other lads would, but these things happen in football."
Reid admitted Odemwingie could have some role to play in the future as West Brom try to halt their current slump.
He said: "Will we welcome him back? We'll have to see and it's up to the club how they deal with it.
"But if it does happen I'm sure we'll get on with it and there might come a point in the campaign when he's needed.
"It's up to the club and I'm not going to get involved in team selection. It's also up to the fans how they deal with it."
Reid believes Albion need to "stop shooting ourselves in the foot" and admits the players felt let down by left-back Goran Popov's red card for spitting at Spurs defender Kyle Walker.
Head coach Steve Clarke confirmed Popov will face disciplinary action in addition to the three-match ban he must now serve.
West Brom had to play the last 42 minutes with 10 men and they eventually succumbed to Gareth Bale's superb strike.
Reid said: "In recent weeks we've been shooting ourselves in the foot and at the start of the second half Goran has let us down with the red card.
"He's obviously given the referee the opportunity to show the red card and, when you go down to 10 men against a team with the quality of Tottenham, it's always going to be difficult.
"Goran's English is spot on to be honest, he doesn't need to say anything because we've had words in the dressing room and we've now got to regroup and go again."