If you want to list the available EXR layers from a node you can look through the outputs sockets and check to see which are enabled.
>>> node = D.scenes['Scene'].node_tree.nodes['Image']
>>> [socket.name for socket in node.outputs if socket.enabled]
['Image', 'Alpha', 'Z']
It doesn’t seem possible. There should be something like below in the image but looking in the bpy docs there isn’t, ask on blendercoders or stack exchange I guess.