Interesting question...also a very difficult question.
First, your posting identifies no names. WHO are you seeking to find in this area that arrived by train from 1890 to 1910? If this is one family, then you MUST identify WHO exactly you seek in order to find WHEN exactly they first arrived. The WHEN is so very important, an arrival date also strongly dictates what route they may have taken from initial departure to arrival. Also, there is a consideration on what route THEY may have taken to visit other family first. As example, did they travel from West Virginia to Pennsylvania to pick up parents? etc.
Looking over your other postings, I find:
Benjamin Pleasant Hawley from West Virginia, in Promise, Wallowa Co, Oregon in 1900. I suspect this is the family you seek? Some factors on the family. I often wonder why after so many years in one place, such as the Hawley family, after having so many children, that they suddenly moved from West Virginia to a wilderness area of Promise, Oregon.
Now, the wide gap in potential years, 1890 to 1910. This gap greatly influences the potential routes they may have taken due to the basic availability of train routes. Even ONE year could influence the routes taken. Even in the SAME year routes changed. If they traveled in July, there may have been more trains on more routes than in January, due to heavy snows in the passes. Even today, Amtrak changes their routes, sometimes on a yearly or even seasonal basis.
Other factors: The completion of railroad lines to various cities. IF they went to Promise, OR, they probably didn't travel by train all the way there. They may have traveled to the closest hub, perhaps Spokane in Washington or Boise in Idaho, perhaps down to Clarkston, WA/Lewiston, ID, THEN by wagon.
I looked at the two links posted by the other. Neither had any information relevant to your research.
Some Oregon Rail History:http://www.pnwc-nrhs.org/oregon-rr-history.html
"IF" this Ben Hawley is who you are researching, it appears he married Abigail Abby Miller in 1896, in West Virginia, but then I also see the marriage as being in 1869(numbers reversed on one of the records?). The 1900 Census finds them in Grouse and Promise Precincts of Wallowa Co, OR. The youngest child was born in March 1896 in West Virginia (Erie T). So, it appears they moved sometime between that birth and the 1900 census.
So, to find out what route they took has MANY factors and will take a lot of work. First to find out exactly when they left West Virginia, who arrived and when. Then attempting to identify what trains were actually arriving in what nearby location.
The Bureau of Land Management http://www.glorecords.blm.gov/
has a database of land obtained under the Homestead Act:http://www.legendsofamerica.com/AH-Homestead.html
The BLM shows Benjamin P. Hawley obtained 160 acres of land on 2/28/1906 in Wallowa County.
First click on "Search Land Patents" (background is green), then enter your zipcode. Enter "Oregon" and "Hawley". Clicking on his name will give you more info on the land. Under the tab of Legal Land Description, it is shown as being in Township 4-N(north), Range 42-E(east), Sections 23 and 26. If you don't know where this land was located, repost and I'll give you instructions.