My family tree is already posted in other threads on this same bulletin Board. All I essentially know is that my Great Grandfather, Giovanni Antonio Ieradi was from Cortale (Calabria), Italy and was born about 1860, as has already been stated.
One of his sons (i.e. Tomaso I(e)radi) ended up in Buenos aires as a young orphaned boy of about 8 years old (because his father had allegedly died there about 1895). Giovanni's other son (i.e. Antonio Salvatore I(e)radi) left Cortale, Italy and immigrated to New York City about 1904.
The Iradis of Venezuela and surroundings were Hispanics - not Italians. There were people with the last name "Iradi" already in places like the Dominican Republic and other Caribbean Islands VERY early on as the result of Spanish conquest, and I believe that a surname search in the database of Ancestry.com will reveal those various names and dates.
I would not be surprised if you were decended from one of those early Caribbean, HISPANIC lines, particularly given the fact that one of your recent ancestors bore the Dutch (i.e. Dutch-Caribbean) prename "Frits".
That being said, the EARLY ORIGINS of the surname 'Iradi" are in the Basque Country in the district of "Iraty" in Spain, as I've already stated. Therefore, those early "Iradi" sailors-colonists-raiders-planters-whatever who came to the Caribbean on Spanish Ships were very likely ethnic Basques.
Hope this helps, and good luck with your Caribbean/Venezuelan search for your Basque-cum-hispanic Iradi ancestors.
DMI