I disable those events in my code in order to override them and provide enhanced functionality. Just blocking them is generally a bad idea; it annoys the user.
But the general approach would be to register for the events you want to block, and call event.preventDefault() to suppress the default behaviour. For ONPASTE, this is trivial. GWT doesn't expose ONCUT or ONCOPY, so you'll need some JSNI for those. I posted some sample code here: