Keep in mind that:
a) As far as I can tell, animals only claim a nest box for the duration it has eggs in it (or is on the way to go lay eggs in it), so just because nest boxes aren't claimed doesn't really mean anything...
and
b) Left alone, your dwarves will quickly collect any eggs from nests (well, as long as the haulers don't have too many other things to do, which might slow them down)
Er, actually looking back again, I see the "locked in a room" which should take care of that, for the crocs at least. I can't tell if the birds are locked in or not, if not, that's probably your problem with those. You either need to catch as soon as they lay the eggs and forbid them, or make sure you lock them completely in. With the crocs, I dunno what the problem is unless they're either not tame (as already suggested), or you thought you locked all the doors leading in/blocked off all the entrances, but one of the doors isn't actually locked, or you have some other way into the room that you forgot about.
So yeah, make sure each door is set to "forbid passage," if you have them to "keep tightly closed" that just keeps animals from wandering in and out, but lets dwarves still go through. And check each one carefully, since it's fairly easy to think you have the cursor on one door when it's actually on another.