I don't think they will stop you from bringing your own soda - we brought our own bottle of wine onboard and bought sodas on the islands for the room with no problem.
I believe you can charge a portion of your gambling money to your room but it has a limit. On the QE2 the limit was $1,000.00. I can't see any need for traveler's checks for the ship unless you don't want to carry any cash. They may be useful in the various ports. The purser will exchange the checks for you into cash onboard, however all costs on the ship can be charged to your room (which, of course, translates into a charge on your credit card).
Hope this helps and have a wonderful time. She is a beautiful ship. Be prepared to walk a lot - she is HUGE!