Is it possible to have common content for several users? For example, sometimes there is a situation when several project's users need to work with common content not using one account for them. 
That is, each member of the group has his own account with his login and password. But they need to have possibility edit and delete data inputed by other member of the group before. 
Are there any solutions which can realize it ? And it is desirable to the solution wouldn't be the Organic Groups module or based on creating of a lot of roles.
And if there isn't the solution, how, by you opinion, is the best way to create this feature ? Can one try to use the Relation module and overriding Access control to perform it ?
Have a look at the Group module (commonly perceived as an alternative for Organic Groups).

Group allows for creating arbitrary collections of your content and users on your site, and grant access control permissions on those collections. It is available as of D7, and has a D8 version also. The Group module creates groups as entities, making them fully fieldable, extensible and exportable. Which also makes it integrate very well (out of the box) with commonly used modules such as Rules, Views, etc.

Some more questions you may want to look at for more details:


What are the various roles supported by the Group module?, which explains the various types of roles that can be used.
What are the features of the Group module versus Organic Group module?


Resources


Community documentation for the Group module.
Video tutorial "How to use the Group module in Drupal 8 to manage editorial access control to different areas of a web site".