There would be a lot of information on individuals who immigrated to the US from Sardinia, but you would have to research each individual separately..
using Google to search for "Sardinian immigration to the US" I found at least one article on the topic https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.2050-411X.1988.tb00573.x
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Dear Ms. Parsons,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located 46 series, 2276 file units & 1116 items relating to Sardinia. Some of the records are digitized and available using the Catalog. For access to the non-digitized records, please contact the reference unit listed in the record description.
Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from various NARA units. We apologize for this inconvenience and appreciate your understanding and patience.
We suggest that you contact the Sardinian American Club of New York “Shardana USA” for more information on Sardinian immigrant communities in the United States, as well as review the NARA’s Immigration Records web pages, and the FamilySearch Research wiki for Italy Emigration and Immigration Genealogy.
We hope this is helpful. Best of luck with your research!
I know this is an old thread, but I hope to be helpful somehow as I was born and raised in Sardinia.
As for the world events, I'm pretty sure you can find records of Sardinian men during the I World War: there was a whole part of the Italian Army called "Brigata Sassari" and they were known as "dimonios" by the Austrian troops, which means demons; others were in Brigata Benevento, Calabria, Catanzaro and so on.
There's a book dedicated to the soldiers from my village who fought called "I caduti oranesi nella Grande Guerra" and some trees were planted outside of the cemetery to honor their lives and remember them.
Regarding the immigration part, I'm pretty sure we can find many information on people from Sardinia who went to the US.
I'll be looking into the matter and post again if I find something useful to your research.