[Elladan and Elrohir]

Just to make it clear, Gandalf does not summon the eagle with his staff. You might say that he signals Gwaihir with it, but the actual summons came from Radagast, who obviously does not appear anywhere in the movies.

I agree with Lathriel that it is consistent for Gandalf not to have his staff on the top of Orthanc, considering PJ adding power to the staffs. But yeah, Gandalf the Grey and Gandalf the White are apparently assigned two staffs each. He seems to lose his staff almost as frequently as Anakin Skywalker loses his lightsaber.