What is most effective use of speciality points in doomsday event?

It will depend on what you want to achieve but one recommendation is to use them in the Blue section to unlock the additional honor structures. (4 unlock points are found at diagonals to the center point). Then once you have done this, and set up your additional buildings by alliance centers, you can respec the points with a Speciality rest token (if you have one) and then put the points into the Red section hitting as many Might and Immunity bonus points as you can.

This will maximise the amount of immunity you can gain and help you hit higher level plots.