This clip from the film Full Metal Jacket gives a sense of the singing character of the cadences chanted by Marines and hints at the complex interrelationship between sexuality and military violence (“I don’t want no teenage queen/I just want my M-14”):

A Date with Chris. The website archive.org has a considerable number of aircheck recordings from armed forces radio (AFVN, or American Forces Vietnam Network). These include numerous episodes of Chris Noel’s show “A Date with Chris,” which exemplify the middle-of-the-road musical fare G.I.s often tuned into. This undated recording features an instrumental cover of the Beatles’s “Hard Day’s Night,” Keely Smith singing “Pennies from Heaven,” Anthony Newly belting out the big band number “That Old Devil Moon,” the Ray Coniff Singers, Ella Fitzgerald, Andy Williams, Carla Thomas, and Noel herself reading letters received from G.I.s.

Town and Country. Here’s an example of the country music show “Town and Country” from 1970, hosted by Don Cotterell:

Dawn Buster. Here’s an example of the daily morning show “Dawn Buster,” ca. 1968-69, when the show was hosted by Pat Sajak (future host of the game show Wheel of Fortune):

In 1967, Edward Lansdale, Senior Liaison Officer of the CIA in Saigon, compiled a mixtape of musical recordings made at his house in Vietnam and sent it to Lyndon Johnson, Hubert Humphrey, Robert McNamara, William Westmoreland, and other top American officials. Titled In the Midst of War, the tape collected fifty-one songs recorded in 1965-66 and was intended to give its recipients a more clear-eyed perspective of what was occurring on the ground in Vietnam. The songs are interspersed with narration read by Hank Miller (written by Lansdale).

Folklorist Lydia Fish wrote extensive notes on the recordings, and they are available here:

To my knowledge, this is the only surviving aircheck of the pirate radio station Radio First Termer, which existed for about three weeks in 1971. It was launched in 1971 air force sergeant C. David DeLay, Jr., under the pseudonym Dave Rabbit.

Here is that audio file courtesy of archive.org

I am not aware of any extant recordings of any of these bands, but in 2007, the label Now-Again released a compilation of soul, funk, and rock recordings by four bands comprised of U.S. Army servicemen in Europe in 1971-72. They give an idea of what some of the CMTS sounded like. The commercial CD release included extensive liner notes. Here are the recordings: