Peggy
I don't believe there was a 1920 census for he was probably at sea when the census happened. If this is your John Vernon Benham he was a seaman but not in the Navy. It looks like a seaman on merchant ships. Here is what I found.
Jan 8, 1920 Ship W H Tilford ( a ship used to transport oil), saling from Antwerp, Belguim to New York. This from New York Passenger Lists. he was listed as a messman in working in a the ship's kitchen. His age was listed as being born in 1897.
Next part how did he get to Oregon? In those days sailors either went around Argentina to get to the west
coast of California or the Panama Canal. In 1920 I would think he came through the Panama Canal.
Here is some more evidence. This is from Oregon Passenger lists 1882-1957.
J Benham, born 1896, (This is evidence but without the first name), he was seaman on the ship Cardigendire,
which was leaving Vancover of Oct 1921 going to the coast of Oregon.
thanks, Jim