Are these eggs safe to eat?
I have heard it stated before, but here it is from various sources:

Source 1

Source 2 (confirms the shake test)

Source 3

In general, the air pocket in an egg gets bigger as it gets older due to the permeability of the shell.  I think the shake test is a little hinky, unless it actually sounds like water sloshing.  I would try the float test; fill a bowl to twice the height of the egg, and place it in.  If it sinks to its side, it's fresh.  If it stands on its end, it's probably good, but needs to be used quickly.  If it floats, toss it.