If Arduino IDE itself is built on Java can I run JVM on the Arduino? If yes how should I do it?
Search for "embedded java". Oracle supports it for ARM cores, which is what some of the arduino-like boards such as the Teensy 3.X have, but I doubt they have enough resources to support it.
There is haiku-vm (google it!) that's designed with AVR processors in mind, but I don't know how actively it is being worked on.
Googling "embedded java avr" yields a tremendous amount of results; did you even try that?