Deleted emails are, usually, not separate files, so they cannot be individually erased, by any program. Essentially, emails are stored in a database. Most email programs have a facility to compact this database, and so remove deleted emails from the files. You can then erase free space to get rid of as much of the old files as possible. However, Recuva (and no doubt other file recovery programs as well) has a remarkable ability to reconstruct an emails database from fragments it finds, so complete erasure can be very difficult to achieve. Moral: don't put sensitive information in emails ...
As to using Eraser, I strongly recommend that you read the FAQ post "Getting to know Eraser 6". But I'm not sure that Eraser is of use for your stated purpose.
If you are using web mail via your browser, the emails do not actually reside on your machine (though elements of them will find their way into your browser cache); you can use the webmail facilities to delete but not erase emails. Normally, deleted emails reside for some time in a trash folder, and are then deleted from the server. You cannot control what happens to them, but the chances are that they then become non-recoverable. You can also usually empty the trash folder at any time. For all of those functions, you need to consult whatever help your webmail provider makes available. As, in such a case, the emails don't get to your hard drive, at least as emails, Eraser is of no use to you for cleaning up after deleted emails.
Some webmail users (including myself) prefer to download their messages to a local email client, and delete them from the webmail server. If you do this, the advice in my previous answer applies.
I think, for as long as you do not control the email server you use, you'll be bound to have a copy of the email lying somewhere (even if it's on the provider's servers.) Of course, we try to be careful where possible, but in some circumstances this is just not practical... just my thoughts.