Linear Circuit and System Interpetation
But given a circuit that contains current or voltage sources, for example, isn't this now a nonlinear system?


It is not strictly a linear system.

But if you consider only its response to an AC stimulus, it may still behave as a linear system.

Therefore we often call something a "linear circuit" even if it is not a linear system.

In any case, we almost always apply linear circuit theory to circuits that are not in fact linear, but that behave linearly in response to perturbations of the input around an operating or bias point. (Physicists talk about perturbation theory as a general method of finding linear approximations to the behavior of nonlinear systems, and linear circuit theory is one example of this)


  A circuit containing resistors with i-v characteristics of the form \$V = IR+V_0\$ where \$V_0\$ is some constant could not be considered a linear circuit and you could no longer employ superposition analysis or Thevenin/Norton analysis, correct? 


You can still do Thevenin and Norton analysis because Thevenin and Norton equivalents apply to networks containing a combination of linear resistors (or impedances if we get into AC analysis) and ideal sources. 

Your "resistor" is basically a series combination of what the rest of us call a resistor and a voltage source. It's actually already its own Thevenin equivalent. And so long as the \$R\$ coefficient isnt' 0, we can also find a Norton equivalent for it.


  Does it even make sense to try to define an input/output of a two terminal device?


We can choose either voltage or current as an input, and the other as output.