You probably have an answer to your question already, but I think I have some info that will help in case you don't.
According to research I have conducted via Ancestry.com and a few other sources, I know that John Joseph Swoboda came through the German port of Bremen to New York in approximately 1857.
There are many variations of the name: Swododa; Svoboda; Swobaday; and Swobody which have been used in this country. John Joseph came from Moravia and used the spelling Swoboda to my knowledge. It is how it is listed on his gravestone.

My grandmother, Minnie (Oliva Philaminnie)Swoboda Stevens was John Joseph's granddaughter by his son Charles Leopold Swoboda. Many members of this family lived in or near Franklin Co, MO. Minnie moved to St. Joseph, MO before 1915 and remained their until her death in 1967. I do not know anything yet about a brother who may have traveled with him. I do know that several of his children were born in Austria including Charles. I believe there were a couple children by his second wife, Anna Nauser who were born in America.
I hope this is helpful. I am really just starting to put the pieces together myself. How are you connected to the Swoboda family?
Hope you are still with Ancestry.com and receive this! I would sure be interested in communicating more with you about this.