OmniLayer got sponsorship from Tether & performed major updates in 2019, releasing major version 0.7.0. This version also changed the code base from Bitcoin Core 0.13.2 to Bitcoin Core 0.18.1. (Omni Core is a modified version of Bitcoin Core.)
Omni project status and plans in this blog post: STATE OF THE LAYER – END OF YEAR 2019.
0.7.1 adds functionality in preparation for a DEX.
0.8.0 is a major release; resolves consesnsus-affecting issues.
The are now up to 0.8.2, released in May, which adds new RPCs for the DEX.
They also seem to be stable after the concerns in early 2020.