Man I feel for you and your parents!!!
To begin with I have no experience with anything like this nor have I ever traveled to that part of the world (this is the disclaimer because I may be about to provide useless information).
If I were in this situation I would:
A)be pulling my agent out of bed and shoving his face into a phone or
B)booking my parents out on the next flight.
I figured I can help you with B.
Disclaimer #2....I have no idea how exhaustively ITN.com searches for flights so it may not give every possible routing.
A search on ITN shows they are probably not getting back to JFK anytime soon. I could not book any flight from DEL - JFK unless it was booked in First and occasionally Biz. Through Europe at least! I don't know if you can get Austrian to endorse the ticket over to another airline or either have them refund the difference and have enough to buy another ticket but just in case you want flight options....here they are. The availability through Asia was very good. Several more flights than the one option below.
Air India #304 DEL - NRT (Tokyo) May 3 20:50 - 8:00 (arrive May 4)
United (operated by ANA) #8230 NRT - JFK May 4 11:00 - 10:30 (same day arrival)
Another thing I would think of would be to get them out of India and to....say London. Lots of flights LHR - JFK. ITN.com inventory showed a very small amount of availability in coach (several First and Biz) on the following flights but I could not book them for some reason.
Air India #765 DEL - DXB (Dubai) May 3 21:20 - 23:05
British Airways #106 DXB - LHR May 4 1:35 6:20 (same day arrival)
I couldn't find anything for the 3rd.
I really hope this helps. Actually I hope they are already on their way and this is a bunch of useless information.
Chris Moss