Hey Yangster. Each of those controllers you listed is a different SATA controller on your motherboard. You would need to refer to your motherboard manual to see which controllers belong to which ports (and which one handles the eSATA port).
I apologize as I should have mentioned this up front in my original reply, but if you change the controller from IDE to AHCI that controls your OS drive, your OS will fail to boot and just BSoD. This should only be done before a new OS installation, as an OS like Vista or Windows 7 will install the drivers for AHCI automatically during setup. It won't harm anything to do it but the system won't boot until the OS drive's controller is back to the setting that was selected when the OS was originally installed. So the DVD drive should be fine!
Performance isn't really an issue for AHCI unless we start talking about SSDs, because AHCI allows for additional commands to be passed to the SSD that are needed for best performance. For hard drives and DVD drives it doesn't matter except to enable AHCI required features such as hot plugging.
One of those controllers controls the eSATA ports for your motherboard, probably the GSATA (Just a fancy name rebrand Gigabyte uses for the Jmicron controller chip) but again you need to make sure via the manual for your board. If that controls the eSATA port AND you are running Vista or Windows 7, then setting that to AHCI should allow hot plugging for eSATA devices.
Your DVD drive shouldn't have any issue with AHCI or IDE. So with the exception of your OS drive it doesn't matter if IDE or AHCI is selected for any devices unless you're using SSDs. AHCI is generally recommended as it's an improvement over IDE, but again the only reason we got into all this was to allow for hot-plugging support.
For all the hassle it's up to you if ya want to stick with USB 2.0 given that's much more convenient to use, the speed loss is there but the convenience factor makes it a tough choice. And as you found out restarting with the drive plugged in is always an option too, you don't need AHCI for that. But, keeping your OS drive on a different controller than your eSATA port(s) will allow you to change the eSATA controller to AHCI without any further issues. And as long as your new OS install is Windows 7 or Vista then the OS should then recognize and initiate the drive when it is plugged in.