Chicago-Vienna-Romania, okay.
Is this a single itinerary, booked as one ticket, or separate booking for the second leg?
If you bought the flights separately, there is a chance that you will have to go through immigration into Austria and then check in to the second flight. The chance of sending your luggage straight through to the final stop is also lower. If a single itinerary, you may be able to simply claim your luggage at the destination.
You can see the advantage of booking a full itinerary rather than patching together several separate flight tickets. Often cheaper, too.
You might check with the originating airline. Also ask about a visa. While Americans do not need a visa to enter the Schengen zone, which includes Austria, Romania is not part of Schengen. Not yet, anyhow, but may apply sometime soon.
Schengen is also developing an electronic locator called ETIAS, not a visa but a trace function for visitors from outside Schengen. It may not be fully operational yet. Anyhow, something else you can ask the airline about.
Sorry it is not simple but that's now travel life -- adding in the Covid travel requirements too which can vary from place to place.