the JRE doesn't contain everything, the SDK does
The JRE is merely the Java Runtime Environment, whereas the the SDK contains the JRE and also all the stuff to develop with.
has stacks of info on how to install the stuff.
What exactly are you trying to do anyway?
The JVM is java itself, so if java runs (type java in the console) then everything should be right, the path to it can be determined with
but really it should be in /usr/bin/java (which is generally a symlink to its real location)