OS services JFK-VIE on a daily basis: OS 88 JFK (T1) – VIE 1830-0915+
As your travel originate in Canada, there is no special rule traveling through Europe, however a maximum of one stopover permitted in any one city. You can do … VIE-BUD-VIE-PRG-VIE-MUC-FRA-CAI...
From CAI you have two options (skipping OS): Going back to FRA/MUC on LH or continuing to SIN on SQ.
Bear in mind that for travel originating in Canada reservations and ticket issuance must be made at least seven days prior to departure for sectors up to and including the first international sector. Other sectors may be booked at any time.
RWSTAR Rules