To keep u-p morale, the US recorded immense quantitites of music, comedy, and general entertainment from all the hot acts and bands of the time, and pressed them on humongous 78 rpm records, "acetates" (18 or 24 inches, sme still in use in to the early 60s) and shipped them overseas, where they were broadcast on local armed forces stations, I think they were in general called the Armed Forces Radio Network. The discs were fragile ang wore out quickly, so a lot just vanished, but there were still hundreds that survived, And news came over to the states via shortwave, to be rebroadcast here. As Contrex says, big band swing and dance music was hugely popular. The government also organized USO tours of top entertainers to do shows ovderseas for the troops, the Andrews Sisters were huge, and they did a number of songs with nilitary themes, Bob Hope and Bing Crosby, Marlene Dietrich, Glen Miller, the Dorseys, all wnet overseas. Glen Miller, I think, also lost his life when the Army plane he was riding in, went down over theEnglish Channel, if I remember right. Google "World War II music radio broadcasts" for some of the stuff that survived.
Get a DVD or the movie musical "South Pacific: from the mid-50s, when they still had a lot of WWII equipment operational. It's got a Hollywood version of a USO show in it, which was probably fairly close to what the troops might have gotten, and I think there's a scene near the end where the French troop spotter Emil deBecque is using a portable shortwave transmitter to call in a re[prt before the Japanese planes come back to strafe him, which imight be original equipment. They did have portable radios (sort of "portable", more nearly "luggable". 15 or 20 pounds, running on batteries, and I think military eequipment included hand-cranked gnerators to run things like radios and maybe recharge batteries). And soldiers listened to other countries' forces radio too, to get an idea of what the enemy might be doing (which is how the Brits in North Africa fighting Rommel got turned on to
Lili Marlene" being broadcast from what /belgrade in Eastern Europe).
If you want authentic atmosphere, there are quite a few CD compilations of authentic WWII sibgs, Great musci.