Running some Java EE libraries or frameworks in non-standard VM is not an uncommon task and same is for Tyrus. I have to admit that this task was driven mainly by issue report TYRUS-256 from Reza. There is no official support from Tyrus running on Dalvik and I'm not even sure if it is a good idea, but important fact is that it works and you can do it if you want :-).
Whole issue which blocked runtime from being able to run on Android was in usage of javax.naming.InitialContext class. There is no simple alternative to it, but fortunately there is always a possibility to do little bit of reflection hacking to get rid of the dependency if it's not there. The rest was only about creating the sample application and testing it on my phone, which was not that hard. I have to give kudos to IntelliJ IDEA team for their support, but not for Android Studio - it uses gradle as build tool and it seems like you cannot include java library because android plugin clashes with java plugin (I'm not very familiar with gradle as you might have noticed). Using and build script and build in support was better for my task.
The application I used for testing is available on github in my personal workspace: https://github.com/pavelbucek/tyrus-client-android-test. Feel free to test it and/or provide pull requests. I would be particularly interested in gradle build script.