I'm a big fan of the Omega base theme, trying to make sense of what's going on with that project.
What I'm trying to do, is work with something similar to Omega 4 that is actively maintained on both 7 and 8 and will be capable of being upgraded to Drupal 8 in future.
I've read that there was a public falling out among the maintainers and that Omega 5 is progressing in a very different direction with different aims to Omega 4. I've also read that the Omega 4 maintainers are giving it minimal maintainence with many hints that their efforts will be focussed on other projects under other namespaces, and there have been no new dev releases since July 2015:
Omega 4.x is still minimally maintained (I am committing bug-fixes and other critical / major patches). However, I am not interested in further moving on with anything under this namespace as stated previously in other issues. The reasons for that are well known and have been publicly discussed... There won't be any extended effort from me (and probably not from Matt either) to expand on the existing functionality of 4.x or even work on a new version... I will keep maintaining the 4.x version of course though so you can totally feel safe when using that at least.
Is there a new project that continues what Omega 4 was trying to achieve under a new namespace, that will be actively maintained on Drupal 7 and 8?
I've seen Khan described as "the omega 4.x successor for drupal 8", but it's had no work since 2014 and its project page is... baffling. It looks more like a Drupal community in-joke than a serious project. There's a thread with many people asking about this, but no clear answers.