I am moving to Iowa for academic purposes but will not be taking a domestic flight directly to Iowa but will be going out from Chicago, spending few days in Indiana and then taking the bus to Iowa. Will this be an issue and will I be questioned as to why I am leaving in Chicago? I heard that strict investigations are done when people do this and that we have to show proof and justify why we are getting out in a place that is not mentioned on the I-20
Very doubtful. The family of Chicago airports are a major hub internationally for many destinations in and around the U.S. There is certainly no rule that an international traveler must always enter at the location closest to their final destination. Many final destinations might not even have airport service anyway. With today's system of competing airlines and online customization of journeys, it's probably not even possible in most cases. You just fly into some hub and find your way onward as best as you can.
You will pass through immigration once, at your port of entry. The immigration officer will probably ask you where you are going, and might ask you to show how you plan to get there. As long as you have a plan (either a bus ticket itinerary, or you can show that you clearly have the means to buy a bus ticket later), then you should be fine. There is certainly no requirement for you to fly to your final destination.