I can confirm what ILUV767 said. My fiance works for UA out of IAD, and she has flown most of the possible scenarios that were mentioned. She has actually done a domestic trip involving 737/757/A319 or A320, and in the same month through trading with someone for an international trip, flown the 777. And I also know that when they were flying 747s to LHR when she was based there, she would work it along with the 777 interchangeably. I have known her to work all of UAs types except the DC10 since we have been dating, but I am sure she worked it at some point before I met her. So yes, they can work any type in the fleet. And yes, she knows every safety aspect of every aircraft. The things she can tell me about each one amazes me.
A woman drove me to drink and I didn't have the decency to thank her. - W.C. Fields