Gary Poulter did not receive an Oscar nomination for portraying Wade in Joe.
Gary Poulter was not a professional actor when he was cast in the film. The casting of non-actors in important roles is a risky endeavor sometimes it pays off in handsomely, such as the Oscar winning performances of Haing S. Ngor and Harold Russell, but that's is not always the case such as Dexter Gordon's Oscar nominated performance or the supporting cast of Gran Torino for example. Gary Poulter actually does share one thing with Dexter Gordon in that both have not necessarily the most cinematic of voices, nor are either of them the most charismatic of performers, a major difference though is Gary Poulter actually has screen presence, Gordon did not. Poulter plays the father of Gary who very much fails to be the father Gary needs. Wade at first we find is an alcoholic, and basically the ugliest sort possible. Poulter effectively plays him as someone who's always somewhat intoxicated, at least the to the extent he can be intoxicated. He's not pained by it nor does he really receive an pleasure from it, but rather Poulter shows it as more or less the natural problematic state of Wade.
This sort of role certainly can be overplayed, look no further than Marco Perella's work in Boyhood for such an example though he was more of a middle class drunk, but Poulter only ever feels very real in his portrayal of this. One great scene for Poulter is one where he is just hanging out with his son, and they technically are just fooling around a bit. Poulter is very effective in this scene by showing that there is a lighter side to Wade. Poulter is good in the moment as he does bring a certain ease and even a bit warmth suggesting that there is a bit of love in Wade, although not much. Poulter though in no way diminishes the more negative qualities in Wade as he still is rather uncouth, and it seems the only reason he's easy to get along with at all is that he happens to have a drink in hand at the time. It's an important scene though as Poulter and Sheridan to establish that there is at least some pleasant moments between the father and son, and perhaps even makes it understandable why Gary is willing to take Wade's punishment even though he has no patience for anyone else trying to push him around.
Wade is not a good father though and Poulter is brutally cruel in the scenes where Wade abuses Gary. Poulter does not show any hesitation in this, nor really any guilt when he slaps his son hard or punches him down. It's a very casual thing and Poulter makes it quite disturbing because he presents it as just standard procedure for Wade to violently accost the boy whenever he has a moment of frustration. There is not a second thought he gives the action but rather Poulter plays it merely as the standard procedure for Wade. What does set Wade off is dealing with any judgments from anyone else such as when Gary finds a job for himself as well as Wade in tree removal company run by the titular Joe. While Gary is much more than a natural in the job, Wade consistently falters in his work. Poulter is excellent in portraying the searing anger in Wade that comes to the surface whenever he is pushed into a corner, but actually being called on his behavior. Poulter brings a raw messy intensity that suggests something very dangerous about such a man.
As Gary becomes closer to Joe he steps away from his father, and stops really supporting him which leads Wade to become even worse than he already is. In his attempt basically to keep getting money for alcohol Wade does some truly evil things. One such scene is when he finds a vagrant with wine and begins talking to him. At first he speaks about his wife dying from cancer, the film does not specify how much of this is a lie, but Poulter is rather moving in portraying the pervasive sadness in the old drunk. That moment of humanity though is abruptly ended when Wade bludgeons the man to death merely to steal his drink and whatever he has in his pockets. Poulter is horrifying in this scene because of how meaningless the violence is in the moment and shows it to be just a natural course for such a desperate man. Wade after taking anything kisses the dead man on the forehead, and Poulter manages to make sense of this in the jumbled mind of such a man. There after all was not true malice in his attack, but rather it was the only way that Wade was going to get a drink.
With Gary away Wade only continues his horrible acts which ends with Wade trying to prostitute Gary's mute sister to a couple of Joe's local enemies. This ends with a violent conclusion for the two men who are killed by Joe in a fight. Wade does not fight back and when confronted by Joe merely asks "Are you my friend?" by Wade. It is heartbreaking moment by Poulter because he does not portray Wade as a wholly evil man, even though he does very evil things, but rather just a lonely pathetic man. It is unfortunate to have to note that Gary Poulter died shortly after the completion of the film. Despite this being his only performance in film Poulter does not give the work of an amateur. He knows how to make an impact in a scene and is able to stand in a scene next to Tye Sheridan and Nicolas Cage. This is a great performance by Gary Poulter because he realizes the complexity of a man like Wade. He's never simply is a one-note drunk as the character very well might have been in lesser hands. Poulter realizes the randomness of Wade into a single cohesive character and creates a harrowing depiction of a broken man.