Go to /System/Library/LaunchAgents and move com.apple.java.InstallOnDemand.plist. That will remove the “Install Java” dialogue.

cd /System/Library/LaunchAgents
sudo mv com.apple.java.InstallOnDemand.plist /tmp

After that make sure illustrator doesn’t need java by removing the FXGFileFormat plugin. Go to /Applications/Adobe Illustrator CS6/Plug-ins.localized/Illustrator Formats.localized and move FXGFileFormat.aip and FXGFileFormatUI.aip out of the directory. Now restart Illustrator and Voila!

cd /Applications/Adobe Illustrator\ CS6/Plug-ins.localized/Illustrator\ Formats.localized
mv FXGFileFormat* /tmp

Tip: Change the illustrator folder `Adobe Illustrator CS6` to your version. Ony