How do I find out which version of org-mode I am using?

You can invoke org-version:

M-x org-version

This should give you the version information of currently loaded org-mode.

You could use the package listing

M-x package-list-packages

Then find down the bottom which 'org' you are using. It maybe under status 'built-in' or 'installed', if you click on org then it will tell you the version.