I had a J1 trainee visa, can I go to Canada and come back with an ESTA?

If you're not subject to a 2-year rule, the only potential problem you may face when returning to the country almost immediately after leaving is that they may suspect that you're going back to work/stay for longer. In such cases, documentation will help you convince the immigration officer of your intention to do tourism: Most importantly, you should have your flight reservation for your trip back to Italy, but of course hotel reservations will further help you make your case.

You can reenter if you have visa waiver status and your ESTA approval. However, as stated above, it helps to have you further travel itinerary booked to show that you aren't trying to reenter to stay and work in the US. If you're using your VWP entry for the first time after your visa expired that should be perfectly fine, although one never knows. Basically, ESTA means that you're eligible to board flights etc. to the US, but it does not guarantee entry. However, it should be ok.

PS. also inform your IO that you're entering on ESTA this time, since they might take a look at the visa and see that your grace period is up and be confused (although that didn't happen in my case).