where can i find the birth dates of my great grandparents

U.S. Immigration and Naturalization records are available at the National Archives in Washington, DC. For access to these records, please contact the Textual Reference Archives I Branch at archives1reference@nara.gov. Many of these records have been digitized and are available via Ancestry.com (http://search.ancestryinstitution.com/search/category.aspx?cat=40) for a fee but are free if you conduct your search at one of NARA's facilities.

Also, since your grandparents were born in Italy, any birth records may be accessed through the Italian Archives for Genealogical Research at http://www.antenati.san.beniculturali.it/en

Oh boy, if you don't know where they were living those citizenship paper could be anywhere, and in all kinds of courts which could drag you from county to state to federal courts! My wife says try this link, they've compiled all that stuff since their start in 1906 and can help.

Genealogy | USCIS