Groucho Marx did not receive an Oscar nomination for portraying Rufus T. Firefly in Duck Soup.
Groucho Marx plays Rufus T. Firefly who is elected to be the new leader of Freedonia even if it takes a while for him to realize it. Who Groucho plays does not really matter as even though his name may be different this Groucho Marx doing his routine as Groucho. Marx's routine is not really to play a character, and his whole thing is to almost be separate from the story at hand. Now it is true of many of the early comics like Chaplin, and Laurel & Hardy in that they would play the same characters in their films, but those characters could still become emotionally involved with the plot of the film. This is not the case of Groucho Marx whose whole bit is to be kinda disassociated with everything to the point that he will often comment toward the camera to voice his insult or general disinterest at anything that is going on around him. That is perfectly fine though as the film is almost wholly built around Groucho's comedic manner to the outrageous situation he finds himself in.
Well Marx certainly is entertaining in his constant cracking of wise throughout the film as he basically never stops making insults of one form or another at anything and all things. Marx's whole method is to be as rapid fire as possible really, and rarely does he stop except for a slightly absurdest reaction to something. Therefore not every single joke he makes is going to perfectly land perhaps but a whole bunch of them certainly do. My favorite instance of his wordplay insults is when Firefly is interrogating a spy (Chico Marx) for the other nation and says everything as positive while twisting it quickly into actually something quite negative. Marx is very purposefully extremely one note in his performance as Marx never changes from his rather disingenuous attitude. Even in a scene where Firefly accidentally gets angry at the dictator of the other nation causing a war, Marx still plays it all the same, which is the whole point of his comedic character, which is just fine since Marx is consistently funny here.
Well what's a comic performance from the period if one does not count the physical aspect of the comedy? Well Marx actually takes a similair approach to the physical comedy as he does his verbal comedy with again being purposefully withdrawn from the whole thing. Marx often has just a big grin on his face, quite enjoying the hijinks himself, while walking around in a purposefully casually goofy sort of way. Marx actually has quite a bit of energy in the big musical numbers, or the scenes of great physical comedy in his manner of not caring. Marx's timing is excellent even though it all seems to lack a technical purpose, it's an odd trick, but one that Marx pulls off quite brilliantly. Now reading just the synopsis of the film you may be tricked into thinking this performance, and film has some greater purpose like Charlie Chaplin's The Great Dictator. That's not the case as the whole idea about the countries is merely just a springboard for some various comedic situations for the Marx brothers to participate in. Marx's performance does not strive to be anything more than it is which is a very enjoyable example of his usual shtick.