First off, welcome to FT and sorry to hear about your cancellation.
Second, I expect this thread will be moved to either TravelBuzz or the Delta forum - perhaps even before I finish posting my reply.
Now, as to your problem. Delta cannot simply order you to fly out of IAD because it is more convenient for them. Since they cancelled the flight, they are obligated to get you a new flight which is acceptable to you. If they cannot do so, they may be obligated to refund your ticket price. I suspect that is not your real goal here, since you apparently intend to take the trip. That scenario would also get complicated because this ticket is not only international, but on multiple airlines. You don't say whether or not the Alitalia flights are Delta code-shares or not, nor do we know which airline actually sold you the ticket (Alitalia or Delta) - it could have been either. You could find those things out by speaking to your travel agent, which in this case is Orbitz.
That's right - Orbitz is your travel agent. So they really should be helping you out here. Now, I am not at all surprised that they have tried to pass the buck to the airline. But I'd call them back first and try to make them help you, before just going direct to the airline. I say that here, specifically, because Delta has outsourced much of their call center operations to overseas facilities who staff are not all as well versed in customer service and Delta's operations as we would like, and if you try to handle this through one of the overseas call centers, you will probably be so frustrated you'll need an extra vacation to recover.
So, long-winded intro out of the way, here's what I'd do:
1. Go to Delta's web site and look up their flight schedule. Find an option which works for you as a replacement flight (perhaps it's an earlier flight out of DCA?). Preferably, find two or three options that might work. I believe out of DCA you could always take the Delta Shuttle to BOS, although that involves a connection at LGA. This replacement flight could also include a change of routing such as getting to PRG through ATL, CVG, or NYC...
2. Call Orbitz back with that info and try to get them to accommodate you on one of your acceptable options.
3. If #2 fails, ask to speak to a supervisor at Orbitz, and repeat.
4. If #3 fails, call Delta and try it.
5. If #4 fails, call Delta and see if the person who answers the phone has a foreign accent. If so, hang up and call again until you get a person with an American accent.
6. If #5 fails, ask to speak to this person's supervisor and try it with them.
7. If #6 fails, have a couple of beers, then come back here and post for more advice.
Good luck...