ok Toby, you are hacked because you didn't upgrade your software (most likely the hack went through old Joomla)
Somebody is messing with your files. If you look through ftp you will see files are changed (look at the dates)
Upgrading now is too late.
Putting down a back-up won't work either.
First you need to get the site completely down right now so your visitors won't get infected.
(if they are without proper virus scan/firewall or on Mac, so they can blame themselves as well).
And also google will not give you more penalties. They don't like infected sites.
Then you need to clean your site.
Your host could be very helpful in finding infected files (or not depending on host)
Or get a pro expert to clean it for you. Someone who can read log files.
Or start your learning curve.
Then upgrade joomla. and all special scripts.
And inform Google site is allright.