Use maps in an application with a closed user group ?

Yes.

Should you create a derived work of OpenStreetMap data (say, a map with a certain map style or certain items highlighted or added), the members of the closed user group to whom you publish that work will have the right (under CC-BY-SA) to use that work and publish it as they see fit, and you may not contractually forbid that. However if they do not have an interest to publish, they don't have to.

Example: You provide a commercial OSM-based map to paying customers only. You don't have to provide the map to anyone else. If your customers have no interest in giving away what they bought from you, then they don't have to; you have your closed user group. But if your customers want, they can upload your map to a web site.

Using something in-house is usually not viewed as "publishing" though.

Yes that is allowed by the CC-BY-SA license and will remain ok after the switch to ODBL. HHowever keep in mind that all your users are free to redistribute the map data according to the license used by OpenStreetMap.

So if you had closed as in "only users who paid me" in mind you might have a small problem. If you were think closed as in "internal map for the police department" then that is ok.