My sites have been hacked by a turkish, alias MiKtOLyN, arkicentral.com, healthopia.info, uparki.org. Please help me. What's the best thing to do. These sites run under joomla.

Updare joomla version. Also you can ask your web hosting service provider how to work on it

upgrade joomla, change all your passwords, hostig, database, ftp etc
ask your webhosting provider to restore the site from bakup if you do not have one yourself

Investigate the way that was hacked in. That could be due to the holes in some of the scripts you are running

yeah alex021 is right, have to restore everything. All the information you have, you have to change passwords, codes, everything.

You need to know the reasons of hack and then act. Of course all the measures must be taken, but that might be not enough unless you know the real reason of that