The name that is most comfortable to me is highway. But, living in areas more rural than where I grew up I use Interstate if it is indeed an interstate, because in less populated areas they still use highway for rural highways. In dense area where there are many interstates and spurs and beltways I sometimes call the interstate specifically by number, for instance I would say I take 95 to 395. I drop the “I” usually.
Sometimes I use the term freeway, but less often.
If the road is actually called a parkway I use that, but I would not call a random interstate a parkway.
Sometimes a section of the interstate has a name, like I87 is “the Deegan” in NY, you put the the in front, and I am used to people calling it the Deega, not by the number. My guess is it was the Deegan before it was part of the interstate system.
Here where I live now there are some roads that are called expressways, they are not part of the interstate system, and I refer to it as an expressway using the full name, selmon expressway, similar to how I use parkway.