Here's a start...
Vincenzo was born in Agnone in 1853. My gg-grandfather, Domenicangelo Orlando, was his older brother (b. 1844). Their parents were Sabatino Orlando and Candellora Venditto. I've only been able to find one other sibling - a sister named Maria Fedela (b. 1846).
Teodora's parents were Carmine Camperchioli and Maria Rosa Li Quadri. Teodora had at least 6 brothers and sisters that I know of: Margherita, Pasquale, Marco, Ma. Vincenza, Ma. Annunziata, and Francescopaolo.
Teodora's brother Pasquale was married to Vincenzo's sister Ma. Fedela.
While I haven't come across a birth record for your grandfather (which doesn't mean much given the condition of some of the records), I do know that he had at least 6 brothers and sisters. Alfonso, Ma. Teresa, and Ma. Carmela were all born in Agnone. Luigi, Ma. Margherita, and Candellora were all born in Chicago according to the parish register for the Church of the Assumption of the Blessed Virgin Mary in Chicago.
You also said that your grandfather went to Chicago at some point to work for the railroad, which makes sense. Domenicangelo and his oldest son Cristanziano (my great-grandfather) both worked as brakemen on the railroad in Chicago. (Domenicangelo died in 1900 in a work accident.)
I have more information on both family lines going back a few more generations that I can send you.