I just installed it on my HP Chromebook (Xfce). I am trying to get OpenJDK 7 on it. When I use the Software Center to install it, it looks like it installed correctly, but when I try to open Minecraft.jar with "other application" I don't see JDK Runtime 7 anywhere, only JDK Policy Tool.
java -version should be enough to know that Java is installed. Java is not actually a program that you use, but a programing language in which people writes their programs on (in this case Minecraft) and gets executed by the Java Virtual Machine, this virtual machine is what executes whatever program is written in Java.
There could be problems if you messed up with environment variables or tried to install Java using a method other than the suggested (using your system package manager) for which you could have problems executing some java programs.