What sensors do I require to detect multiple objects on a board
Well, there are few requirements listed, so here is one of many completely arbitrary possible answers.

Use peg board with infrared sensors looking through the holes. 



You'll need to have a microcontroller (likely with a few slaves) scan the sensors in a grid-like fashion. You'll be trying detect the presence of something blocking the hole, for instance, a post-it note.

That meets you requirements you've listed, but I can't see how you're going to get from here to possibly detecting anything written on the notes. Perhaps you should start with that in mind and work backward from there.

If only you had some sort of method for tracking your progress...