There is a way to view your bank and shared bank from anywhere in game but... since SOE took steps to remove one method for doing this, I'm not going to point it out directly. Some info on this can be found on this site
Haven't found any way to view the house vault away from home.
It is probably possible to dump the tooltip inventory list for any Bag/Box into your log file via the chat window. You'd have to setup buttons to do this and the info wouldn't display in-game, only in the log file.