"The Greys are a bunch of hit-and run guerrillas; when I was little, my dad used to scare me at night by telling me stories about the Greys. You don't have to like the Greys, but you gotta respect them..." - Sarge
The Grey Nation is the nation with the least amount of attention of the Army Men series, only appearing on some games as enemies and sometimes as allies. Unlike the other nations of the Plastic World, the Grey are not as well definitely based on a real world nation until one remembers history.
The Grey plastic army takes or took its influence or inspiration (according to the original creators) from the civil war plastic play-sets with the Grey representing the Civil War era Confederacy. Their beleaguered state during the onset of the events of Army Men PC and from some citation from the 3DO staff hint at the Grey Nation as an amalgam of WWII era Russia but in a weaker capacity just as the Greens represented as an underdog America in the PC games. Also, the guerrilla tactics employed by the Grey are reminiscent of the Vietnam War era Viet-Cong.
According to some recent sources from the internet archive and the concept discussions of the 3DO staff, the Grey Nation was once a powerful nation of proud warriors whose pride became their downfall when they were invaded by the Tan; they were too sure of their might to ask the Green for help when the Tan were conquering their country. Now, most of their country is occupied with the Grays staging guerilla war to win back their homeland. If we make educated inferences from the first Army Men games (Army Men for the PC and Army Men 3D) the opening video states about the natural geography of the world; "from the northern mountains, to the western desert, and as far as the southern swamps." then most of the Grey Nation is in the southern lands. The reason for this statement is that in Army Men 3D during the Bayou campaign you have what is heavily implied to be Grey settlements, weapon factories, and the occupied Grey capital at the end of the game. The colonel in the bayou level had a house in the swamplands and the weapons facility you retake from the Tan has unfinished Grey tanks. With the opening letters to the last missions stating something about the capital and the presence Grey and Tan forces engaging in combat throughout the city and cemetery, then it is very logically possible that the city was the Grey Capital under Tan occupation and that the majority of the southern bayou region is the Grey Nation itself. Also, in the real world, plastic army men with a Grey scheme were typically associated with the American Confederacy in contrast with their opposing color the blue and even the creators of the Army Men PC games used this influence at least partially in making the Grey Nation.
The first encounter with Grey forces is in the original PC game: Sarge is attempting to outflank the Tan and finds himself on the Grey-Tan border. Whilst both are at war with Green, they are also at war with each other and Sarge finds himself in a three-way shooting match. In Army Men 3D, a Grey Colonel is captured in one of the last missions. The Grey Army is located in the western, southwest, and southern part of the Plastic World because it borders the Tan nation (which according to Army Men: World War lies in the Western Part of the World).
In Army Men: Sarge's Heroes, they appear as prisoners of the Tan Army that can be freed by Sarge (The Player) to help him rescue Shrap. Colonel Grimm makes a direct mention of them in the level's intro cutscene.
In Army Men: Sarge's Heroes 2, they make minor appearances, one being during the Assault at Dr. Madd's Castle as enemies working for the doctor and later during the Tan invasion on the peace signs where the player can see two Grey soldiers fighting the Tan Army with no avail.