I think this is a bit of a red herring - the book is funny throughout and the humour is not dependent on a deep knowledge of the sociopolitical climate (which, incidentally, was not yet quite 'Stalinist'). I first read it in my mid-teens (in Russian) and didn't catch a bunch of that stuff either - but it was funny. Just like you don't need to know an awful lot about 19th century Britain to grasp the wry tone and irony in Austen or Dickens.

Try reading the Burgin/O'Connor translation and see how it goes. It's possible it might still not work for you but an audiobook of some unknown translation is an unfortunately pessimal way to approach this particular work - you're now dealing with not one but two layers of interpretation of a difficult-to-translate book.