how can you relate users to each other? (like all belong to a team or company)

Well, it depends on what the system is supposed to do with the information about the user's role and company. I suggest you take a look at http://drupal.org/project/og, it's got a lot of functionality for handling groups and group specific permissions to post and read stuff.

OG's do not nest one within another. So OG's will allow you to group people (loosely, as group members can choose when to leave a group), but one OG cannot join another, so you have only one level of an organization. You can't build hierarchical relationships of groups.

You might need to create an elaborate set of roles to describe all the types of users, then mis-appropriate the taxonomy and taxonomy access modules to control access to pages based on roles you assign to users.

I am also looking for an elegant way to map real-world rights, roles, and complex associations into Drupal access permissions without hacking existing modules to death.