Common shell / editor shortcuts for Mac OS X
This is definitely possible, see https://developer.apple.com/library/mac/documentation/Cocoa/Conceptual/EventOverview/TextDefaultsBindings/TextDefaultsBindings.html for a good discussion of text system key bindings.

To accomplish what you're after save the following to ~/Library/KeyBindings/DefaultKeyBinding.dict:

{
    "^u" = "deleteToBeginningOfLine:";
    "^w" = "deleteWordBackward:";
}