Will the factory wooden stock taken from a M77 tang safety 338 Winchester Magnum fit a Ruger M77 7x57 ?

If they are both tang safeties it should work I do believe the barrel channels well be different.

The MKII stocks are different and well not work with tang safety actions.

Yes definitely the actions are the same; as stated the barrel channel is slightly larger on the 338.
As for fitting a tang safety into a MK2 stock. I do that all the time. Have to mill out for the tang and get a new floor plate.