Part one: Socialist Realism in popular music in the 30s
So, the style of music you're talking about right now is Socialist Realism. Starting during Stalin's rise to power, Socialist Realism was a set of do's and don'ts applied to all sorts of art- not just music, but also art, film, theatre, and writing. It's important to note that the main purposes of Socialist Realism were:
In music, folk songs were the ideal genre to turn to. Western musical styles were frowned upon, especially jazz. Tsarist classical and Romantic-era music was condemned (although this would change during WWII as the Soviet Union strove to promote a sense of Russian patriotism), but folk songs were well-known by the masses, easy to sing and memorize, associated with the lower classes as opposed to art music (I use the term here instead of "classical music," as "classical" refers to a specific time period), and supported the Socialist Realist purpose of idealizing this class of people. One of Stalin's primary goals when he first took power was his first Five-Year Plan, which involved industrializing as soon as possible. To do this, he believed that agricultural land needed to be collectivized in order to provide food for a massive workforce. While peasants who refused to collectivize were persecuted, the kolkhoz system needed to appear appealing- not only to the peasants, but also to workers and intellectuals who were skeptical of the system. By using a musical style associated with peasants that also evoked nostalgia for an earlier time without recalling the Tsar, the collective farm was easily romanticized. For example, here is a Socialist Realist song in Yiddish (with English translations) that talks about how good life on the kolkhoz is, and here is another in Russian about a peasant girl who is rejected by her lover, although the tune is upbeat and the lyrics are catchy and repetitive. "Catchy and repetitive" is key when it comes to any music intended for a mass audience- think of, for example, modern pop songs. Repetition makes a song easy to memorize (note the "oy-yoy-yoys" and "ay-yay-yays" in both songs), and also more appealing. Take this piece, for example, "The Song of the Counterplan," which, while musically very simple (especially for its composer, Dmitri Shostakovich- remember that name; we'll come back to him later), was is upbeat and optimistic in both its lyrics and music, and became a hit song both in the Soviet Union and abroad.
Military music has the same effect of being simple, repetitive, and easy to sing. While the folk songs created a sense of nostalgia and romanticized peasant life, military music displayed the glory of the Motherland, which the people had fought to create. As for choral music, this was heavily promoted in the Soviet Union as well, starting around as far back as the 1920s under Lenin. Choral music, of course, requires a large number of singers who all work together to sing the same song, appealing very much to that Communist ideology. By combining the patriotism of military music, the camaraderie of choral music, and the nostalgia and idealism of folk music, Socialist Realism had a very effective formula in terms of stirring the revolutionary sentiments and pathos of the people.