They run Dalvik, which is Googles proprietary VM. Its similar to the JVM in purpose, but it is supposed to avoid Oracle's patents and has a few specializations for mobile.
AFAIK (I'm not a java developer), any language that can target the JVM can target Dalvik.
AFAIK, the only language that's officially supported by Dalvik is Java, and code in other languages tends to run into limitations in the bytecode-to-Dalvik translator.