I have a Joomla site that has Search Engine Friendly URLs turned on but Google keeps on picking up urls with the index.php in it and sometimes with index.php/index.php in it. I already submitted them for deletion and they where processed but they have returned.
i'm not an expert with joomla since i prefer to use other cms. it seems to me that you should double check your settings & maybe also check out the htaccess file.
another tip is to check out your log files. it can help you if you know more about where these urls are coming from. is another website linking to you with a typo in the url? maybe one of your internal pages is broken and linking to these urls. these bad urls could be formed by many different ways. if i were you i would peek into the log files to see if there are any clues there.