Speech often doesn't matter very much in this book. Either there's nothing to say, or there's nothing anyone can say about various injustices, or there's nothing anyone really wants to say in the freezing cold. So we get an emphasis on actions instead, which really do speak louder than words here, reluctant as we are to endorse clichés. Alyoshka is characterized by his praying, Shukhov is characterized by his extreme work ethic and his clever plans, and Fetyukov is characterized by slacking off and mooching. Given that this book occurs over the span of one day, and given that we spend a lot of time inside Shukhov's head, the little habits and gestures of our characters become very telling.
Clothing is definitely a sign of status in the camps. The guards and the wealthy prisoners with connections wear nice fur coats and hats. The average zek, on the other hand, wears a basic black uniform and is generally freezing. But there's an important commonality among everyone in the camp: numbers. All prisoners must wear a number, no matter how well-off they are, and all prisoners are called by their numbers by authority figures like the guards. It's dehumanizing ultimately and it helps to emphasize how all the prisoners are basically in the same boat.
Nearly all characters in the book have some sort of nickname (like the guard named "Snub Nose" who comes to collect Buynovsky at the end) or a descriptive phrase attached to their name, courtesy of Shukhov. Sometimes this refers to where they are from, like the two Estonians who basically have no other names. Other times this describes who they are, or a defining characteristic: Buynovsky is "the Captain," Alyoshka is "the Baptist," Fetyukov is "the scrounger." Still other characters are defined largely by their job in the camp: Tyurin is "the foreman" while Limpy is "the mess orderly." Titles and nicknames do a lot of work characterizing people here, and for certain characters that we only encounter briefly, nicknames reveal how other prisoners think of them. Most of the wardens have mean nicknames, for instance.
As with clothes, occupation is definitely a sign of status in the camp. What's interesting though is that this doesn't reflect the outside world. Take Fetyukov for instance:
You don't need brains to carry a handbarrow. That's why the foreman had put these ex-bosses on the job. Fetyukov was supposed to have been a big boss in some office. Went around in a car. (320).
In the hierarchy of a prison gang, a peasant/carpenter/bricklayer like Shukhov is given "skilled" jobs while a former big-shot like Fetyukov is given the most menial tasks. Shukhov's work skills are a particularly crucial part of his character.
Occupation also reveals who has money or influence, or some combination of those things. Tsezar worms his way into a cushy office job, for instance, since he has lots of money and can bribe people. We also frequently hear about other prisoners who have bribed or scammed their way into jobs where they get to take advantage of other prisoners, like the kitchen staff who takes all the best food for themselves.