Applying for a post-graduate degree with an Italian three-year bachelor's degree
It is standard practice in the US for students to apply for graduate programs before they have received a degree, and the TOEFL exam is normally taken as part of the admissions process.

However, you should also be aware of the fact that you have largely missed the admissions "window" for this coming fall: at most American graduate schools, you need to apply during the previous fall. So, for instance, to apply for admission in September 2014, you should have applied during the period (roughly) September 2013 to January 2014.

It is unlikely you will be able to secure admission to any American graduate school starting this September. At best you will be able to apply for admission in the fall of 2015. The only exception will be schools with "rolling admissions," which accept applications at any time.

As for the acceptance of the "triennale" degree, you will need to ask the individual schools you're interested in; I'm not aware of any such master list (because the number of recipients of such degrees who enroll in any particular program probably isn't big enough to support such a list).