You should have a phpbb_smilies_bak table in your database. The mod (or you) should have created that during installation. That contains the smilies table from before it was altered. Use phpMyadmin to change the phpbb_smilies table name to phpbb_smilies_new, and then to change the phpbb_smilies_bak table name to phpbb_smilies. Together with putting back your backups, your forum should now be back to the way it was.
@Mickey14: thanks for pointing that out, I'm sure it is either a partial install by Easymod or a sloppy manual install. In both cases the way forward is usually fastest by going back to square 1 and doing it properly