Dyre (1859) and Thomas (1864) from Luster to US?

Dear Listers! Another big challenge for you today, which has rested on my desk for more than 40 years: Johannes Torkildson Ronnei/Kalhagen (1832-1914) and Ingeborg Andersdotter Hunshammer (1830-1901) farmed for a few years the Kalhagen farm in Luster County, but later became «husmannsfolk» at Hesjebakken under the neighboring Ronnei farm. They lived and died in Norway. However, they had two sons who have disappeared in America: * Dyre Johannesson Ronnei/Kalhagen, born in Luster Co., Norway June 6, 1859, emigrated in 1883 * Thomas Johannesson Ronnei/Kalhagen, born in Luster Co., Norway Dec. 28, 1864, emigrated in 1884 As the story goes among relatives in Norway, one of the brothers shall have lost one arm in an accident as a young man, and then one of them is supposed to have resided at Williston, ND in the 1920's, but neither of these facts have been possible to verify! Any chance one or both of them can be located in America? I would be very happy for any suggestions and thank you all very much in advance! Very sincerely yours,