First of all, I'll have to tell you that this works on steam when purchased mostly on "PC" platform.The processes might not be the exact same thing with PS3 or Xbox, but give it a try anyway,unless i suppose it has asked you when joining in-game. There are 3 different costumes for each character, but before i speak about those, some characters ex. Helena, Piers and Sherry do not seem to be in the DLC content that you probably bought. So you will have to unlock those first.

Characters unlocking:

Hellena Unlocking: Play as any character on Urban Chaos stage and reach B rank or higher. B rank for "solo" is 80000 - 99999 Score and Duo 120000 - 179999 Score

Piers Unlocking: Play as any character on Steel beast stage and reach B rank or higher. B rank for "solo" is 80000 - 99999 Score and Duo 120000 - 179999 Score

Sherry Unlocking: Play as any character on Mining Depths stage and reach B rank or higher. B rank for "solo" is 80000 - 99999 Score and Duo 120000 - 179999 Score

After Unlocking The 3 Characters it's time to move on their costumes that are called EX1,EX2,EX3

EX1 Costumes Unlocking on Mercenaries Mode:

Leon Unlocking: Play as Leon on any stage and reach A rank or higher. A rank for solo is 100000 - 139999 and Duo 180000 - 219999

Helena Unlocking: Play as Helena on any stage and reach A rank or higher. A rank for solo is 100000 - 139999 and Duo 180000 - 219999

Chris Unlocking: Play as Chris on any stage and reach A rank or higher. A rank for solo is 100000 - 139999 and Duo 180000 - 219999

Piers Unlocking: Play as Piers on any stage and reach A rank or higher. A rank for solo is 100000 - 139999 and Duo 180000 - 219999

Jake Unlocking: Play as Jake on any stage and reach A rank or higher. A rank for solo is 100000 - 139999 and Duo 180000 - 219999

Sherry Unlocking: Play as Sherry on any stage and reach A rank or higher. A rank for solo is 100000 - 139999 and Duo 180000 - 219999

Ada Unlocking: Play as Ada on any stage and reach A rank or higher. A rank for solo is 100000 - 139999 and Duo 180000 - 219999

Now, to get the EX2 costumes you will have to head over to residentevil.net and register there another account, which is not from steam but Capcom. On the top side says Login/register click there and click the next time register and put your e-mail. After that you will have to confirm that the message that has been sent to is yours. After making the validation process you will have to put all your info in there, example: Date of birth, Password, E-mail e.t.c, Steam, PC platform and do not forget to write em on a paper in case you might need em. So do not complain about that i did not warn you.After following these steps login to your account and then you will have to link the account of capcom with steam account. To do so click on "overview" and somewhere there it will say "link with steam account" or something like that, then click there and enter your steam informations. After that your Steam account is now connected with capcom.
After linking to the account and clicking "Game items" you will see each characters EX2 costumes and it says 60000 REP. You will have to earn those through by competing or cooperating with someone in-game and/or earn web badges and medals + the chance to login every day will give you some bonus REP points. After collecting enough of those 60000 rep it wants you can purchase it and play with in the game.

For the EX3 Costumes you can see them by pressing the EX3 Costumes beside EX2. To get those you need to participate in "every day online event that is announced to take a ticket and purchase one costume of your choice.

To participate in a online event
1)You need to have capcom account connected with steam account
2)Enable the "Auto Data Upload" before joining in the game and which can be found at options
3)Connection to your internet is needed so that the progress you have made can be sent to Resident evil site and be written through the event name's that are listed.