I cannot write an essay for you, but I can point to specifics that deal with the theme of loneliness and isolation in John Steinbeck's Of Mice and Men.
George is a lonely man. Having promised Lennie's Aunt Clara that he would watch out for Lennie when she died, George shoulders the responsibility of caring for this very big and strong man, with the mind of a child. They run into problems because of Lennie's child-like behavior, and George has to deal with them. He hopes to have a place of his own someday.
Lennie is not lonely, but he is isolated. Part of the reason for his isolation is that he gets into trouble with others, by doing things that upset people, though Lennie is innocent of any ill-intent. They are run out of the town of Weed because George tries to touch the soft dress of a girl. The gesture is misunderstood, and the pair have to flee. At the end of the novel, George warns Lennie not to speak to Curley's wife for fear that there will be a misunderstanding—when he does, it goes tragically beyond a misunderstanding.
Because of the Great Depression of the 1930s, many people had lost their jobs and homes. Because of this there was a great migration of people moving across the country, looking for work. Because George and Lennie are like so many others in the country, they have no place to call home and must move to find work—or to avoid trouble Lennie has inadvertently caused. It is a lonely life living on the road and moving frequently.
The bunk house is like a hotel: it is filled with bunk beds. One wall is made up of a large door. The other three walls are covered with windows. There is a table in the middle and a stove to the side. This is a place where people come and go. They do not live here, but bunk down while there is work and/or leave when the work is done or they want to move on. Ironically, though there is a group of men living there, the men are not a family; the bunkhouse is simply a place to rest until it's time to move on. Being in the company of others does not guarantee that one will not be lonely.
Loneliness is a way of life that the men at the ranch understand better than the friendship that binds Lennie to George.
Even Slim, who is usually sympathetic and understanding, expresses surprise. 'Ain't many guys travel around together. I don't know why. Maybe ever'body in the whole damned world is scared of each other.'
Another character who is extremely lonely is Curley's wife. The tragedy at the end of the story is due in large part to her need to talk with someone, to connect to another human being. She does not like her husband and is full of ideas of what her life could have been like had she not married Curley. When Lennie says he cannot talk to her, she responds:
Wha's the matter with me?...Ain't I got the right to talk to nobody?
Lastly, Crooks must be the loneliest, most alienated person on the ranch. He is black, in a widely racist society. An old man, he lives alone, working the stables and bunking in the harness room. He has no dreams of deliverance and expects no one else's dreams will come true either, including George, Lennie and now Candy's dream of owning their own place.
This is a story of great loneliness and isolation. Even in the midst of all that George does for Lennie, his only reward is caring for another man, never finding a place of his own or companionship.