It's well known that the Strugatsky brothers were affected by the censors overseeing the publishing of their work.
How did those experiences reflect in their books?
The question is about the censorship experience being part of the content, not the changes made as attempt to pacify the censors.
This subject is covered in most detail in the book "Limping Fate". Unfortunately, there is no English translation yet. This book is written in a form of two interleaved novels (not unlike Master and Margarita). The first novel, sometimes published separately under the same name, describes a few days in life of a Soviet writer. The second, also published separately as "Ugly Swans", was mentioned in the comments to your question; in this book it is a secret and unfinished Magnum Opus of the writer.
The writer bears some resemblance to the collective image of the Brothers: he writes SF (though most of his published works are military prose), he served at the Far East as a military translator, and so on. Among the events of his life, both contemporary and past, the motive of censorship indeed appears from time to time.
In the past:
In '52, the Armed Forces received an order to destroy all ideologically antagonistic literature. Our regiment had a trophy library of some Manjurian noble... Naturally, no-one had the time to separate chaff from wheat... In spite of the strict orders, the literate officers picked some books from the flames...
In present:
Some of the questions HR asked my daugter were pretty weird. What did I tell her about my pre-war Leningrad friends? Did she see any of them personally? ...
"Father, did you do anything wrong?" - A terrible thought hit me: what if they printed me again in another country without the Writers Union approval?
...
Valentin told me that The Quarterly Observer wanted nothing to do with him after the last troubles. In The Provincial News no one had an opinion on his book. They were waiting for the boss to return. When he does, the opinion will magically appear... I asked him, will he fight for the name. To hell with the name, he replied, let it be The Old Sage instead of The Old Fool, but he'll keep the rape scene: let them cut it out, they get paid for it...
However, for the most part the book mentions censorship only in passing, and anyway it was written in the 80's when the censorship got relaxed.
