I'm going to assume since you mention U.S. History that you are in high school?You didn't mention possible ages of the people you are looking for but your age makes it iffy that your grandfather was born before 1930.I checked and unfortunately no James or Jim Torgersons are listed in New York.Unfortunately there are a lot of Torgersons listed in New York including several from Norway that could possibly be Jim's family. I'm assuming his father came from Norway since you mentioned being a fourth generation immigrant.
If your grandmother is still alive I would recommend calling her even if you don't think she likes talking to you.Even if you aren't close to her I'm sure she would give you some information.If nothing else she should be able to give you James' birthdate and his parent's names which would be an immense help plus their marriage date.She might even know when his father came to the U.S.To track someone without that personal knowledge you really need to get beyond the 1930 barrier online.Now is the time to ask while the people with answers are still alive.If I had asked my questions when I had the chance as a youngster (I sure didn't think about it then) I wouldn't be tearing my hair out searching now.Give her a call because you should know your heritage!
Regarding Norwegian culture....women didn't start changing their last names until the early 1900's.Until that time they retained their maiden names after marriage.And of course once they came to the U.S. they took their husband's name even in the 1800's.The problem with tracking people in Norway is that the men changed their last names.For instance my grandfather was named Johan Torgerson, his father was Torger Olson, his grandfather was Ole Johannson.And in many cases also took the last name of the farm they were living at.For instance, my grandfather was actually listed on the records as Johan Torgerson Stole while his brother was Johannes Torgerson Lunde.It does get less confusing after a while.
The good thing is that Norway kept very good records and generally the people didn't move around a lot like they do in the U.S.Once I found my grandfather (came over in 1911) I was able to trace his family back to the early 1700's very quickly.Norway also kept track of who was leaving the country so your great grandfather should be listed on their Emmigrant Protokollar.And since you mention New York, very possibly he would be listed online with the Ellis Island records as well.
Let me know if you get more information and I will help all I can.