This I do not know, but I would guess that the list I linked to above was compiled from the "Utvandrede" sections of the Våler church books, so if you don't find Anton in the "Utvandrede" sections of the Romedal church books, you most likely would not find him in such a secondary list either.
Concerning the Stræthammer name: If you look at the map, there are nearby farms Stræte and Strætkvern, so to me "the hammer by the Stræte farm" would make the most sense.
"Statsarkivet i Hamar" means "The National Archives in Hamar" Hamar is the biggest city and the administrative centre in the region. The meaning of the name is the same as for Hammeren, the city is surrounded by knolls. The city name originates from the medieval farm of Storhamar.