I hope to travel by train to Versailles on Christmas Day. Will the RER B/ RER C train run in the early afternoon? Will there be limited or terminated service due to strike?
On weekdays there has been slow but regular RER C trains from Paris to Versailles Chateau Rive Gauche, throughout the day / afternoon and if that continues to hold true, then Christmas day (a Wednesday) would be no different. (Paris train services run throughout Christmas normally and do not stop for holidays).
Alternately you can take the Transilien L line trains from Gare Saint Lazare to Versailles Rive Droite, which have been running more consistently during the strike. You can read a bit more about this on the Versailles section of the Paris train strike page.
Update: Transilien, the group responsible for the RER C to Versailles and the Transilien L train to Versailles Rive Droite, just announced they will close all trains at 6 p.m. Dec. 24 until mid-afternoon Dec. 25 when train services restart. More information about their schedule will be released on Monday 5 p.m. Paris time.