Get the app called 'Boxcar.'
Your e-mail addresses must have the ability to forward a copy of new mail AND keep a copy in the in-box.
Set up each account in Boxcar. It will send you a push noification when you get e-mail, and you can set a different sound for each account.
I don't think you can use custom sounds, so this is not 100% what you asked for, but it does offer many built-in choices and you can pick a different one for each account so it'll get the job done.
(Since you're getting push notices you can technically set all your e-mail accounts to 'Manual Fetch' instead of timed fetch or push. However, I like to set mine to 1 hour fetch. That way, if I accidentally miss a push notice I'll at least be notified within the next hour as a safety backup.)