I've dealt with this at home when a neighbor started renting out a room through Airbnb. It turned out pretty quickly that our building's documents don't have a direct ban, but there's a clause about "using the apartment for its intended purpose" and "ensuring neighbors' right to peaceful enjoyment of their property." It turned out that was enough to work with.
Here's the short version of the process: first, definitely check your building's charter and internal regulations (like others have already suggested). At the same time, collect written complaints from everyone bothered by the noise and mess - you'll need these for the management company. Important thing: complain specifically about violation of quiet enjoyment and sanitary standards, not just about the rental itself. In Russia, many cities have passed local ordinances banning short-term rentals in apartment buildings - check your local administration's orders.
If the charter and local rules allow it, the management company can fine them. If that doesn't work, you can file a complaint with the housing inspection or go to civil court over the violation of neighbors' rights. Court takes time, but that's what actually works in the end.