I live in Illinois. My childrens' father was convicted of a class 2(1count) and a class 4(1count) felony and is still serving time. I would like to know if he is going to be able to visit our children when he is released?

Probably yes.
It depends on many factors. For example-Bigamy is punished in some states as a Class 2 felony.

I don't think those felonies would bar him from seeing his kids. It would be a sexual predator felony that would bar him from seeing them alone.