Thanks so much for the suggestions. It was in this obituary record that the town was mentioned:
Source: Wetzel Democrat, New Martinsville, W.Va., Thursday, Jan. 12, 1939
Nicholas Hoffman of this city, died at his home on Wednesday, Jan. 11, 1939. He was a retired car foreman for the B&O Railroad Company, having been here for the past 26 years. He came to this city from McMechen, W.Va. Mr. Hoffman was born in Obenshania (Obenshain), Germany on July 28, 1877, the son of Nicholas and Elizabeth Hoffman. He was united in marriage to Miss Louise Maltz of Obenshania, Germany and to this union two children were born. He is survived by his wife and two sons, Nicholas H. Hoffman and William R. Hoffman, both of New Martinsville, W.Va., and one sister, Mrs. Susiana Gibson of Miami, Florida. The remains were brought to the Wharton Funeral Home and prepared for burial and returned to the residence on Thursday, Jan. 12th, at 11 o’clock. The funeral services will be held on Saturday morning, Jan. 14th, at St. Vincent de Paul’s Catholic Church. Rev. Father Garrett will say mass. Interment will be in Northview Cemetery, New Martinsville, W.Va.http://www.wvgenweb.org/marshall/obith.htm
My great grandmother was Susanna Hoffmann Gibson, sister to the deceased. She was born in 1892 and died in 1979. According to this obituary, Susanna's father was named Nicholas Hoffmann, but I've also seen him listed as Ignasius Hoffmann. Susanna's mother was supposedly Elizabeth Malz.
Someone suggested to me that Obenshania could have been a part of the former Austrian Monarchy. And Susanna used to say she was from Austria/Germany. (I've not had any luck finding the right Susanna in ship manifests or immigration records.)