you should not replace the mysql_real_escape_string with addslashes to avoid SQL injection.
if this server config is ON, you need to see slashes before the qoutes. If not, you can test with a simple form and $_POST. If you use addslashes on an escaped value, you then need to see double escaped characters.
if magic qoutes is on, use
mysql_real_escape_string(stripslashes($input));
on your user inputs.
When you build a query string to the database, \' and \" converted into ' and " when this value inserted into the table, so you will see normal ' and " signs when you query down the data.