Hi,
Yes you can check your bags all the way through, as long as it is a through ticket which in this case it is! You won't get a boarding card for the VS sector from BA and vice versa. You will almost definatley find that you will have to produce your bag tag receipts (don't leave check-in withouot them) as VS (and BA on the return) will ask for them as neither airline will have access to the others check-in system.
Hope this helps
Regards Bluejay
Regarding the ownership of the ticket, VS are just fobbing you off as it will be the airlines rules that count on the day as expedia will have nothing to do with your travel apart from the physical taking the money and issuing the ticket.
Tip for next time - fly BA all the way and your highest baggage allowance, ticket status etc will carry all the way through, your bags will be checked all the way and your boarding cards issued for both sectors.
Sorry another bit i have just remembered - you may need to pick your bag up in JFK and put it on the transfer belt (in the same baggage hall I beleive) this will only be required to satisfy US Customs.
