Richard Burton did not receive an Oscar nomination for portraying O'Brien in 1984.
Richard Burton who died soon after completing the film barely received any awards attention for his performance despite it being his last film performance. I suppose the academy was more interested in Ralph Richardson for a posthumous nod. Burton death soon after this is not surprising considering his very haggard look, in fact I would say Ralph Richardson looked much healthier than Burton despite being much older. Burton's physical state is most certainly noticeable here to the point it must be mentioned, but it really does not harm his performance.
In the early scenes Burton is mostly in the background of the film as just another man in their grey world. Burton eventually has a little more screen time as a man who suggests, and seems to encourage Winston to rebel. Burton keeps the mystery of the character intact as there is no reason to really suspect of anything, but at the same time he does suggest that maybe Winston should not go all out in revealing things to him. Burton does not get all that much to do until in the third act of the film after Winston finds himself as well as Julia the woman he was having an affair with caught by Big Brother, and brought in for re-education.
The man who re-educates Winston is Burton's O'Brien. Burton is the epitome of coldness here as O'Brien. Burton commanding voice works perfectly here as an inescapable voice of control. Burton shows no play in O'Brien he will not be fooled by Winston at any point, he will change Winston's mind simply as that. The torture scenes are extremely brutal and Burton only succeeds in amplifying this as he portrays O'Brien as having no hesitations whatsoever in creating as much pain for Winston as he wants to get Winston's mind the way he wants it. Burton's manner is perfect in these scenes creating personally the inescapable oppression that Winston cannot escape from.
This is not Burton's greatest performance by any means but it is a worthy performance to be his very last in a feature film. This is a performance here that does show his considerable talent he had though, and makes use of it well. Burton uses some of his greatest assets here in his creation of a man without any humanity, and only purpose in life seems to make others fit the view of the state. He brilliantly personifies the Big Brother with his performance that is properly overwhelming, as he makes O'Brien a force that not only cannot be reasoned with, but as well shows that the breaking of Winston is simply an inevitability.