Is there any way of entering non-linear material properties into Ceasar, in order to get plastic stress output?

Sorry, but "no".

One for the next upgrade then..!

Not likely, that would be pretty much a complete rewrite of the solvers.

None of the B31 codes use this more involved approach to analysis...

A question is why do you want plastic strain? The B31 criteria are intended to result in shakedown to elastic behavior after the initial cycle(s). If you are looking at elastic followup, people have done simplified assessements of that by reducing the elastic modulus of the portion of the system subject to elastic followup, to evaluate how the strains redistribute in the system.

Dr. Bechts comment brings another item to my mind. CAESAR II is a simple beam element program. The type of affect you are talking about is usually quite localized i.e. may not occur around the entire circular beam element so as such you may even have the incorrect tool to look at localized conditions....

Three dimensional models known commonly as FEA come to mind.