Java and JavaScript are two separate things. Java is a programming language that has to be downloaded and installed. JavaScript is a browser based scripting language that is automatically provided by probably every browser out there. JavaScript is not experiencing any vulnerabilities and doesn't need to be disabled. Java is getting all the attention and should be uninstalled. This article gives a pretty good summation of the differences and what is being recommended.
Should I disable Java, and if so, how?
If you're having difficulties removing all traces of Java you could try a free uninstall utility called JavaRa. There are several "download" buttons on the JavaRa homepage so make sure you select the right one (screenshot provided.)
Hopefully JavaRa will remove the control panel icon. If it doesn't, you could try reinstalling the latest version of Java and see if the control panel icon is functional again. Your choice if you want to keep Java installed or not. I think most security experts are recommending that it not be installed.
java.com: Java + You