Clean up infected files on my website from being hacked

My web hosting service has found many infected files recently from my website being hacked. The files have been quarantined. My hosting says this....... "As such I'd recommend that you re-install' the wordpress core files, and all plugins files from clean sources, after backing up and deleting the current contents. If the scripts/plugins are not cleaned up /updated and the site continues to be exploited, we will have no other option than to disable the site until such time as you are able to do so, as we can't continue to run exploited scripts on our servers. In your case these are old, and your site itself looks to be more or less up to date. So you could probably get away with just removing the infected files, or replacing them with files from the core download. (You don't want to just REMOVE some of the files as they are important for security, like the wp-content/[login to view URL] for example, its supposed to be an empty file.)" "It looks like this site has been hacked for quite a while. The automated malware scan only checks files that are a week old or newer (and thus it scanned your backup that was just generated). However running a full virusscan on the site reveals the actual damage." Please can anyone help?