Igor,
I travel a lot as part of my job, and have never seen a station wagon (or 5-door combi, as you call it) on a rental parking lot. It's just not a very popular car configuration in the US.
Now, you might be able to squeeze your box into a full-size car (most of them have a folding rear seat), but you definitely will NOT be able to put two more people and their luggage in the car. I assume all of you will have luggage if you come to stay for 3 weeks?...
Considering that the three of you will probably share the costs, get a minivan. Rental companies will probably try to talk you into an SUV - but those don't have nearly as much space (they only appear big on the outside).
And don't wait too long - according to my quick search 5 minutes ago, the Enterprise Rent-A-Car at the Indianapolis airport is already sold out of minivans for the desired dates...
If you run into problems trying to find a van, e-mail me (you have my email).
--Mike