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.
BTG Developer santos177 has been working on a port of OmniCore to BTG.