Let me give you a few references to check. First is familysearch.org. Do the advanced search. For last name: Bloedorn; for relationship: parents. For father: Carl, for mother: Caroline Klegin. This will give you some of the children. Then change the father's name to Wilhelm and search again. Finally, do a search with Caroline's last name spelled Klegien. This will give you everyone but Emilie, for whom I found no birth record. However, you'll find her on the ship's list, also her marriage in Dodge County, Wisconsin. She was the only family member who didn't go to North Dakota; she went with her husband to Nebraska, where his brother was living.
I originally found the family in the IGI using "old" familysearch and doing surname searches within batch numbers to find siblings. Only just now tried the new website for this family--much easier to search.
For the ship's list, search Caroline Bloidow or Bloedow. Caroline and five of the children arrived in New York on the Fulton on 25 Oct 1869. Jenni is the person who found this list; see her post from 2010.
As for William and son Carl/Charles, I believe that they are the two Carl Bloedorns who arrived in New York on 24 May 1869 on the Borussia. As you'll have noticed from the christening records, William's full name was Carl Friedrich Wilhelm, and son Carl/Charles was named after his father, all three names. So far, I haven't found Herman's arrival; I'm thinking he may have come over first.
To cross-reference the family, please search Blodorn in Dodge County, Wisconsin, in the 1870 census for the four children living at home (Herman, Anna, Minna and George). Eliza/Elise married August Berndt, who's listed in William and Caroline's household in 1870.
Two of the children appear to have died young--there's no record of them in the U.S. that I can find. Perhaps there are death records for them in the church book(s) which contain the birth and christening records.
I've learned from my research that there were three Bladow families (the spelling of the name they all finally decided upon) that went from Dodge County, Wisconsin, to Richland County, North Dakota. I'm sure they must be closely related to one another, but I have no idea how.
Please let me know if you have any questions about the children. I hope you enjoy looking at the transcriptions of the original birth and christening records.