searching for family

My greatgrandparents immigrated from Norway but we have no information about them before their arrival in the USA. My greatgrandfather's name, as it appears on his death certificate and census records is George T Omli, born in 1845. However, I saw his name as Thomas Omli in an old local newspaper. My greatgrandmother is Julia Thompson, born in 1869. I am not an experienced genealogist, but I want to trace my family as far as possible. Can anyone help or offer suggestions? Thank you.