Right since I'm West Brom too.. like always xD I'll help you out I guess
Out of the players you have listed I believe you should flog all of them except maybe Scharner. He is a good backup for Mulumbu if needed - You can sell Scharner the season after if you want since there will be some good Defensive Mids up for sale or even on a free.
Everyone else on the list you can just flog since they're useless.
As for Odemwingie, he is good for around 2 seasons, I barely used him as a striker, I always played him on the wings to add pace. But I would advise you keep him for a season at least.
Now the players I would sign are Petar Zanev - really good left back for so cheap! I got him for 800k at the start. Way better than Shorey or Mattock too!
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Bressan - A promising midfielder and can be signed for 1m from BATE. The Second season I had some bigger clubs bidding for him at around 7mil.
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Ruben Yttergard Jenssen - Good creative midfielder! Signed him for 2.9mil and so is a good investment considering his age!
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Darwin Quintero - Everyone always suggests him and I can see why! He is a goal machine! Signed him for 2.3mil from Santos Laguna, scoring 30 league goals in his debut season and won top goalscorer award ahead of Rooney by playing fewer matches. Buy at all costs for your strike force!
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For the right back position I actually just stuck with Steven Reid & Billy Jones, they did a good job too. Second season though I signed an unhappy Kyle Walker (Absolute god!) for 3.8mil from Tottenham! Arsenal were reported to be coming in with a bid of 33mil at the end of season 2, but they never did, wouldn't have sold him anyway.
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As for the wingers, I stuck with Brunt one the right wing - Did really good and chipped in with a high amount of goals. And I also played Graham Dorrans on the left wing and he also did very well! James Morrison can add adequate cover too if needed, so can Gera.
But I advise you to offload Gera after the first season since he's on the decline.
Also I signed James Forrest from Celtic in January, first season for 1.9mil, He has a high potential so is a bargain at 1.9mil.
So to sum up this is my Transfer history for the first season - take into consideration the dates I signed the players because in January I was given more money to spend for my high league position, so that's how I could afford them all
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Hope this somehow helps you out a little bit, if you need more help with West brom then i'm here! Life long fan :')