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.