Is "roger" equivalent to "Ok"? I hear it in war movies, movies like Star Wars Clone Wars, and in war games.
It's not necessarily military, it's more radio slang.
In certain radio alphabets Roger stands for the letter R, which in radio communications stands for received.
"Roger" means "I have received all of the last transmission" in both military and civilian aviation radio communications. This usage comes from the initial R of received: R was called Roger in the radio alphabets current at the time, such as the Joint Army/Navy Phonetic Alphabet. It is also often shortened in writing to "rgr". R is Romeo in the modern NATO phonetic alphabet.
Yes, roger or roger that means message received. From Merriam-Webster:
used especially in radio and signaling to indicate that a message has been received and understood