A journal kept in southeastern New England refers several times in the
middle of September 1908 to smoky skies at sunrise and sundown. The
writer learns the smoke comes from "the Western fires." Where were
these fires, how big were they, and when did they start and end?

Mccook --

The forest fires were in what most of us would term the "upper
Midwest," involving northern Wisconsin and upper Michigan.  On Sept.
21, 1908 fire destroyed Foster City, MI, a town owned by the Morgan
Lumber Co. at the time, according to the New York Times on Sept. 22,
1908.

The same newspaper report says that Lake Superior "is almost
surrounded by fires which stretch for hundreds of miles."  Dense smoke
on the lake caused ships to use their foghorns.

The fire was reportedly endangering the towns of Niagara, Ingallis and
Faithorn in Marinette and Menominee Counties in Michigan.  The NY
Times said that an estimated 7000,000 feet of standing timber was
burned in Point Abbaye (just east of L'Anse, MI) on the 20th and 21st.

Though the weather was hot and dry that week, a report on the 27th
indicated that heavy rains that day had put the fires out.

If you use a Google search strategy with the phrase "fires of 1908"
(in quotes), you'll find that the summer of 1908 had forest fires in
West Virginia, New York and even western Massachusetts as well.

Google search strategy:
I used the New York Times index (it's available via my public library
on the Proquest Historical newspapers service) to search initially for
"western fires."  It produced one brief story, so I went back and
searched for "Upper Michigan" and found the Foster City story.

A search involving the following terms will yield information about
lumbering in the area and the involvement of the Morgan family in the
development of Oshkosh, WI.  Unfortunately I couldn't find any other
Internet links to information on the fires:
"Morgan Lumber" + 1908

Best regards,

Omnivorous-GA

Thanks, Omnivorous, for the thorough and helpful answer