I’m making this odd pyramid shape for a woodworking project. I will be using 19mm MDF for the installation, but I am not able to figure out how to cut the bevels of the different pieces. How to go about this?

I edited each object and gave it the 19mm thickness you want. Then using the neighboring objects I traced where they intersected to figure out the bevels and erase the waste. I did convert the groups to components and, since the two triangular ones on each side are symmetrical, I use Flip/Copy to copy the left hand ones to make the right side. The other thing I did is align the component axes so that if you run a cutlist for the model you’ll get useful dimensions.