I think I've come across some clues about Christian's immigration to America.
In The Alsace Emigration Book, Vol. I by Cornelia Schrader-Muggenthaler, published in 1989, there is a mention of a "Chretien Oberle" leaving for America in 1849 (figuring by my records to be about 18 years old).He's listed on page 184.I haven't actually seen the book yet - gotta go through interlibrary loan - but this name was in a passenger index book at my library.
Christian Oberly is also mentioned on page 39 of the Index to the Naturalization Records of Stark County, Ohio (1809-1852).There is a genealogy department at the Stark County, Ohio Library, and I ordered a copy of said entry.Of course it's handwritten and a very faint copy, but here it is to the best of my deciphering:
"Stark County, Ohio Naturalization Common Pleas Journal, Vol. 21, page 223, Saturday, December 11, 1852
"Be it remembered that ...Christian Oberly, alien and citizen of the Republic of Switzerland (and others I'm not listing here) ... came and in open court made oath that is in good faith their intentions to become citizens of the United States, and to ... and abjure all allegiance and fidelity to every foreign prince, potentate, state or sovereignty whatever and ... to the several governments to which they respectively now are citizens of subjects all case not..." end of page.