MySQL data modeling help
I would use separate tables for the project-sponsor and event-sponsor relationships.  You are making two many-to-many relationships here, and that just seems like the right way to do it to me.

Can each project/event/org have more than one leader?  If not, why not simply put the leader id in the project/event/org table?  Otherwise, I would use three tables for the same reason as above: you are describing three many-to-many relationships.