Without knowing the places of birth and death, it's hard to identify these people. As you know, there were lots of immigrants named Nelson.
Do you know whether the Martin NELSON b. 1 Sep. 1893, was born in South Dakota? Do you know when and where he married and died?
In 1900, there were Martin NELSON, b. Feb. 1855, Norway, and wf. Martha in Lake Co., SD, but there was no son Martin.