There are several type of Class 3 items that are restricted by the National Firearms Act.
Each state can impose additional restrictions on the sale, purchase, and transfer of class 3 firearms in addition to the compliance that is required with the national Firearms Act.
In Illinois you can own the following items that are regulated the the National Firearms Act
There does not appear to be a direct prohibition of Any Other Weapon’s (AOW) but some or most AOW’s appear to be banned under additional terms of the Illinois Statutes. In addition, certain C&R firearms appear to be legal. Technically these are not considered to be restricted under the NFA.