If you want to get the major version of the OpenStack (such as Kilo, Liberty), you can check the nova REST API for API version. The maximum version (called "version" in REST API) for Kilo is 2.3, for Liberty is 2.12, for Mitaka is 2.25 .

You can use the openstack client to get a list of API version supported by your cloud but I don't think that those are necessarily going to reveal what version of each service is running behind them.
Why would you want to know anyway? In theory, as an end user, all you should care about are the capabilities offered to you, not the implementation details behind the curtains.

Yeah, in theory, you should only care about API version, but in practice, even slight package version mismatches can wreak havoc though... DAMHIKT

You can use this command to get nova release: nova-manage version