Examples of astrophysical objects NOT in virial equilibrium? Astronomers always talk about astrophysical objects being in virial equilibrium (e.g., a stellar system, or a disk of gas within a galaxy, etc.). But I never hear about thermodynamical equilibrium. 

What are some examples of objects that are not in virial equilibrium?

One example question: suppose that what you thought was a disk of rotating gas within a galaxy (as revealed by spectroscopy) is actually a bipolar outflow of gas. Would the bipolar outflow of gas be in virial equilibrium? 

Is a radio jet (length of hundreds of kpc) from a supermassive black hole in virial equilibrium?
Not clear what the initial part of your question means. Objects can be in virial equilibrium without being in thermal equilibrium.

A clear exception to the virial theorem would be any system that is gravitationally unbound. So you couldn't apply it to a supernova explosion or a dissolving cluster of stars.

The examples you quote are not self-gravitating, bound systems, so no, the virial theorem would not apply to them.