Any suggestions on car rental companies.
It'll be expensive if you can find one. A rental car with Czech license plates will have to be transported back to Czech Republic before it can be rented again. You will pay for that and then some.
But run it by Autoeurope and see what they say.
In addition to what Sam says , consider that the European rail networks are so good ,that unless you have some compelling reason for renting a car , trains are faster and far less stress .
There is always a large drop off fee when returning a car to a different country. Call Autoeurope in Portland, Maine. Train may be best with this itinerary.
You could get one of the Cesky Krumov shuttle services to pick you up in Prague, see C/K and drop you in Salzburg. Pick up a rental car there to see the.incredible Austrian Alps--ending in Innsbruck.
Why is this question in "Italy" ??