icosphere passes through all planes even with collision on in physics tab See animation below:

Red ball passes through everything.

Blue ball passes through both stairs and green plane but finally collides with blue plane.

I have been trying to fix this problem for 4 hours now.

Blender file: 

Animation: 

Physics:


Blue plane, green plane and stairs all have the same physics with just the collision on (no settings changed): 
Blue ball and red ball have the same physics, collision and soft body turned on:
I think you need to simplify the physics models.  Here is what I have for the blue ball and then the stairs:





I didn't change any of the soft body parameters, using the defaults instead. I did set the stairs to Passive and made sure the blue ball was active.

Since I didn't tune the rigid body parameters, the balls tend to pass part way through the stairs, but they do bounce and roll down the stairs.