I understand that you can easily mix groovy&java, clojure&java, whateverJvmLang&java.
Does this also mean I can have clojure and groovy code interact as well
As long as the languages in question actually produce Java classes (that is: classes that are known to the Java platform, not necessarily written in the Java language), then yes: they can easily interact with each other.
At least for Groovy I know that it's entirely possible to write classes that can be used from "normal" Java code.