This post was going to be a question but, after troubleshooting for ~3 hours, I solved it but I still wanted to post it since I am pretty certain that this solution will save someone else time when they encounter this issue and search for posts like this.
I was upgrading my workflows that automatically test my OpenStudio SDK code on a remote Linux machine but I found a huge number of dependency issues when trying to use OpenStudio 3.0 on Ubuntu Xenial 16.04. From what I can tell, some of these issues seemed impossible to address with sudo update commands. However, as soon as I switched to using Ubuntu Bionic 18.04, virtually all dependency issues vanished. There weren't even any issues with libwxgtk3.0-0 that Julien mentioned here.
Granted, all of my tests were using the SDK Ruby bindings directly and I didn't test the OpenStudio CLI or Application. But I have not reason to believe that these wouldn't work.
Long story short: OpenStudio 3.0 + Ubuntu Bionic 18.04 = No obvious dependency issues
