Customs

If you want wine shipped home, you have to ask at the shop where you buy it. They package it up and ship it for you. (they will let you know the fee). I have not had wine shipped, buy my travel buddies have and they did not think the fee was too much.
I have had pottery/ceramics shipped from Deruta - several of us living in the same city had ours all packaged together and it was very inexpensive.
Sorry I don't know about wine.....but I will bet that others on these threads have had wine and also olive oil shipped to the states.
Best of Luck

I think the limit is still ONE liter of alcohol per traveler over the age of 21, not two liters. Please check the US customs website again. You can bring more, but you have to pay more. Yes you can have wine shipped at home. Not sure about the limits for that.

Olive oil contains no alcohol, therefore that is not included in the limit.

Thanks Roberto, I did reconfirm and it is ONE liter of wine.

The bigger issue is, Can wine be shipped to a private resident in your state? The wine shop will NOT know or care about your state regulations.

In practice, bring as much wine home as you can safely carry and declare it on your U.S. customs card. We've brought back as much a 4 bottles per person, which makes it 3 liters. Although that is technically 2 liters over the limit, in practice it is too small of an amount of money to make it worth the customs inspector's time to collect. So typically they will say "Have a nice day". They have bigger fish to fry these days.

It is rarely worth the hassle to haul wine to the US where you can buy a huge range of good Italian wines and not have to fiddle with this. Shipping wine in many US states has to be done through a registered importer and the rules vary from state to state; you can't just ship a case home most places. Also anything you ship is not included in the $800 exemption; it is all dutiable. On the other hand if you want to bring a case back on the plane, you can easily do it and people are rarely asked to pay duty on an obviously personal selection of wine. They can charge duty, but usually don't for a few bottles brought in by a tourist.

I stopped doing this long ago. I think it was the time I sat behind a passenger who got a shower of wine and olive oil from the overhead compartment where another passenger had stowed his badly packed wine and oil. The wine was bad, but the oil worse. Of course these days, you can't carry alcohol in the passenger cabin, but it can still cause a real mess if you carry it in your luggage. I know people whose entire suitcase was saturated with limbic beer they were bringing back from Europe.

I can buy dozens of Italian wines in my city and I'll bet you can in your as well. And I can also choose from a couple of dozen of imported olive oils.

When you ship a package home, Customs will usually clear it through automatically, without collecting duty, if it is for personal (not commercial) use and valued under $200; or a gift to the addressee and valued under $100. That also assumes that the item is otherwise legal to import without a license, etc. This is separate from the $800 duty-free allowance of goods that you can carry with you.

Are you asking about Italian customs or customs in some other country? You have posted this under Italy, so it is totally ambiguous.
If you are entering Italy from another EU country, there is no limit to goods bought for you own use.