Edward McEvoy of Newark, NJ

[Lisa in California]

Perhaps Thomas moved to New York for work?  Looking at the 1880 census (just Thomas’ image page), four other men also had the occupation of Japaner.

[Irish Connection]

According to the 1880 census
Edward - born Ireland, as were parents.
Margaret - born New York City, parents born Ireland
Ella - born New Jersey, father born New York(?), mother born Ireland
Katie - born Astoria, father born New York, mother born Ireland

Was there a mixup with the childrens’ parents’ birthplaces or ?   

I'll have to tentatively accept that the enumerator mixed up some of the birthplaces. They are listed as daughters of Edward on the 1880 census (not sure if the category stepdaughter existed), and I can't find any other "Ella" born in NJ in the 1870s that would match, other than the Elen of Edward and Julia.

The Japanner occupation, although I'm not sure how common, does certainly seem to connect the Edwards - I'll look into that. Thank you for helping connect the dots 

The only definitive way to confirm might be through a record of marriage, depending what information would be on it. Finding it will be easier said than done, though!