I did a bit of searching on this with the information you provided and found the family tree with the two censuses attached [1920 & 1930], as well as, the WWI Draft Card attached to Nicolas...
..."assuming" that the WWI Draft Card attached to the family tree is the correct one for your grandfather and going by the information contained within it...
I found the 1910 Census where it shows Nicholas living with a brother, Pasquale, and a few other boarders.
1910 United States Federal Census
Name:
Nick Vario
Age in 1910: 35
Estimated Birth Year: abt 1875
Birthplace: Italy
Relation to Head of House: Brother
Father's Birth Place: Italy
Mother's Birth Place: Italy
Home in 1910:
Mercur, Tooele, Utah
Marital Status: Married
Race: White
Gender: Male
Year of Immigration: 1901
Household Members:
Pasquale Vario 24
Nick Vario 35
Frank Campisano 21
Frank Rulle 23
Thomas Davis 23
Then, I set out to find ship manifests for either Nicholas or Pasquale... I found one that might be on the right track [Note: according to the 1910 Census, Nicholas was already married]
Ellis Island website
First Name: Nicola
Last Name: Varia [This is perhaps what the original surname was]
Ethnicity: Italian
Last Place of Residence: Cortale
Date of Arrival: Mar 15, 1902
Age at Arrival: 31y
Gender: M
Marital Status: M
Ship of Travel: Citta di Torino
Port of Departure: Napoli
Relative he is going to join in the USA: brother Pasquale
Manifest Line Number: 0015
I searched for Pasquale's WWI Draft Card...I couldn't find one using "Vari
o", so I searched using "Vari
a and found it:
World War I Draft Registration Cards, 1917-1918
Name: Pasquale Varia
County: Tooele
State: Utah
Birthplace: Italy
Birth Date: 18 May 1889
Race: Caucasian (White)
FHL Roll Number: 1984055
According to their WWI Draft Registration Cards: Ophir, Tooele - Utah is the same place of residence for both Nicholas and Pasquale.
In Pasquale's card it shows his birth place as: Cortale, Catanzaro - Italy, which is the same town listed in the manifest info I found
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Liz