As the qustion asks, how informed were Allied troops of operations across the continent. Did the Allied Powers try to keep their soldiers informed of victories to keep morale high?
The people of the Allied nations were kept informed about the goings on in other regions, and that certainly includes the 'going-on' of the Western and Soviet forces for the other. I'll focus on knowledge of the Western Allies of Soviet accomplishments, but that is simply because I don't have anything handy that is similar for Pravda or Red Star to the indispensable primary source I'm drawing on here, namely "The New York Times' Complete World War II" which provides essentially the entire coverage of the war from 1939-1945. Having the "Stars and Stripes" archives of course would be a step better even, but their online archive costs $$, and I don't have institutional access best that I can tell. So the below is a clear demonstration of what information was coming to the West, but I can't say that the troops would be seeing these headlines verbatim, even if it was information they would generally have gotten to read.
So, preamble dispensed with, the New York Times was covering the Stalingrad campaign, both the ups and the downs, extensively throughout. Annoyingly, whoever designed the damn CD did a terrible job and I can't get it to tell me how many articles mention "Stalingrad" within a time frame, but there are a number of them! On July 6th, 1942^1 , within a week of the launching of Case Blau, Negley Farson was writing that "SOVIET OIL SUPPLY HELD NAZI TARGET: Hitler Said to Stake All on Cutting Off Army of Caucasus from Rest of Russia". Although a long drive from Stalingrad at that point, and still only on the outskirts of Rostov, the article discusses the strategic danger that German success might wrought:
Rostov is the gateway not only to the Caucasus but also to Astrakhan, at the head of the Volga delta, to which all oil tankers from Baku must eventually come. It is also the southern land gateway to the Urals, and unfortunately Rostov is only 250 miles from Stalingrad, on the Volga, at which point German shore batteries could sink any oil barge that tried to come up.
A month later, an AP story that the NYT carried warned that the Germans were closing on the city - "NAZIS SWEEP ON IN CAUCASUS AND ADVANCE IN DON ELBOW, STALINGRAD LINIE DENTED. The opacity of the reporting quite clearly illustrates the cagey hold on information by Soviet sources, which prevents a clear picture, but nevertheless the Soviet dispatches that are being drawn upon admit begrudgingly, for instance, that "The Germans threw in many reserves, and only at the cost of heavy losses pressed back our troops somewhat" in the case of one dented counterattack.
The next month, a blasting headline from a Moscow correspondent, Ralph Parker, proclaims that "'RED VERDUN' HOLDS: Greatest Nazi Onslaught Kept from Advancing by Volga Defenders, and breathlessly details the "gigantic struggle for the city", with Soviet forces finally bluntiing the German advance, although still at that time - Sept. 5th - by no means certain. A week later, the editorial section of the Times gave its thoughts on the battle for the city whose fall "would be a disaster not only for Russia but for all the United Nations," laying out the myriad ills it might bring upon the Allied powers, from the severing off the USSR from much of her oil, to emboldening Japan to enter the conflict in Siberia. It is quite plain that not only was the World watching Stalingrad, but also quite invested in the outcome as well, and praying for success.
And when success came, it was quickly know. The first reporting in the volume of Operation Uranus, launched on Nov. 19th, are datelined four days later, from a United Press dispatch crowing "NAZI ARMY IN PERIL: Two Russian Forces Are Advancing North and South to Trap Foe". By the time American readers were seeing the headline at the breakfast table, the envelopment had been completed, but only just. Even in success, of course, the Soviets remained tight-lipped with some details, with the AP noting only on Jan. 1, 1943 that:
The Russians declared officially for the first time today that 22 enemy divisions in the area of Stalingrad had been tightly encircled by the Red Army and announced that 312,650 German and satellite soldiers had been killed or captured thus far in three great drives by which the iron ring was wielded around the ruined Volga city in six weeks.
Although even so, at that point it seemed a poorly kept secret, and one which correspondents had already been giving as fact, with several articles through December on the Red Army's advances, and the Axis' futile attempts to "cut the net", as one Dec. 14th article headlined it, reporting on approximates and educated guesses prior to Soviet announcements. Through January, the end was counted down, and by the end of January, daily updates of the impending collapse tracked that "NAZIS 'WRITE OFF' STALINGRAD ARMY" (Jan. 27), "BERLIN SEES DOOM OF STALINGRAD UNIT" (Jan. 28), and "100,000 Listed Killed, 46,000 Captured in Last 20 Days" (Feb. 1), with the last article additionally reporting the capture of Paulus, based off of reports taken from Moscow radio broadcasts.
Finally, of course, the victory itself was reported almost immediately - one might speculate that successes up to then were kept close to the chest by cautious Soviet sources not wishing to hail success prematurely, but no longer concerned as such - with the German capitulation announced on Feb. 2nd - STALINGRAD ARMY IN VICTORY MARCH - and noting "Marshal Paulus's surrender early yesterday was made in an atmosphere of anticlimax in the gigantic 23-week battle, in the last 10 weeks of which the Germans lost 250,000 killed."
So the long and the short of it is that Americans were certainly informed about the Eastern Front. Nowhere near the depth that was possible for their own forces, nor always with openness from Soviet sources - especially for bleaker events - but an American audience would have been little trouble to follow the highlights of the fighting between Hitler and Stalin, and of course to revel in those blows struck against the Nazi war machine.
Edit: Frustratingly, I can not find accessible archives for "Stars and Stripes". It is all paywalled, and not in the archives I can access. But I don't want my efforts to be for nothing, so at the very least, here is a selection of headlines, all from the last few days of Stalingrad, from various newspapers that are available in ProQuest's Newspaper archive (although many are variations on each other):
New York Herald Tribune:
LA Times:
Reds Capture Marshal and 17 Generals: Russians Liquidate One of Two Pockets Before Stalingrad
Baltimore Sun:
Washington Post:
1: A note on dates. The date is sometimes the byline, sometimes the publication. The DVD is terrible inconsistent, but I've tried to go with publication date when possible since that reflects when Americans would have read it, rather than when a correspondent might have wired the piece.