Can't reinstall osx, messed up partitions.

The following will only work if your iMac is from Late-2011 or later. Let me know if yours is earlier than that.

Clean Install of El Capitan or Later on a Clean Disk

1. Restart the computer. Immediately after the chime hold down the Command-Option-Rkeys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the drive (usually, the out-dented entry) from the side list.
5. Click on the Erase tab in Disk Utility's main window. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to Mac OS Extended (Journaled.)
8. Click on the Apply button, then click on the Done button when it activates.
9. Quit Disk Utility and return to the Utility Menu.
10. Select Reinstall OS X and click on the Continue button.

This should install the version of OS X that was pre-installed when the computer was new.

Oh, My!! You have messed up quite a bit. Yes, out-dented refers in your case to the entry named Fusion Drive. With any luck, this will give you a Fusion Drive that is erased to which you will reinstall OS X. Remember for afterward that a Fusion Drive should not be partitioned except if you create a Windows partition using Boot Camp Assistant.