Thank you so much for your replies and resources.
I will definitely go through all the posted links here and clean my server.
As far as logs go, I don't have access to them, but my web hosting company does. Unfortunately, it takes more than 1 day usually to get a response from them. What I did a few days ago is to just delete those files off the server and wait for them to show up again so I can accurately pinpoint to a small timeframe and get the logs to check.
As soon as I discovered this issue initially, the first thing I did was to delete all FTP accounts and just keep the one, and change its password with a completely new one never used before (which wouldn't work if I have a keylogger somewhere...)
Will let you know as soon as I get more details, maybe finding the issue will help other people as well.
Thanks!