Post a picture of the front of the wall, rather than the side of the wall.

I would try some expansion joint stuff you would use for concrete. Just shove it in the spaces.

I would be afraid of applying any form of caulk or spray foam, which would be impossible to clean up.

They make the expansion stuff in rubber and other materials. It can easily be cut to fit in the spaces.

With a little effort you could mould chicken wire or a finer metal mesh to insert and fit the area to close it off from nesting.

Hard to tell, when the picture is from the side. Looks like a window there with shutters and the arrow is pointed towards the back of the shutters.

Try backer rod first.

Either remove the shutters or try stuffing with brass or stainless steel wool or copper mesh.