Special:Log page lists all special actions (Move, Block, Patrol, etc...) and can be viewed by user. Similarly, the
Special:Contributions page lists all edits by user/IP. I'm not aware of any way of getting the list of user log on/off times or even the last log on time in the default installation of MediaWiki.
If looking at extensions there are likely a few existing options or making your own. Just a quick search revealed LastLoginTime, SpecialLastUserLoginEx, and UserLoginLog. How well these work or not is another matter.