We had a super cruise last September on Oriana. We carried on a bottle of champagne and wine to celebrate our anniversary.It passed through security with us without any problem. Enjoy your cruise!
There are normally 2 formal, 2 semi formal and 3 smart casual nights per week and you should receive exact details with your tickets. The dress code applies to all public areas after 6pm. P&O reserve the right to confiscate alcohol taken on board but is rarely implemented and you should not have a problem. Think it is there to cover the likes of teenagers taking crates of beer on board and getting drunk.
I think that Brian has probably answered your question but just in case you meant the main dining rooms as opposed to the cafeteria style restaurants, the two main dining rooms are open every evening, you will be allocated a table in one of these and you can dress smartly for any and all of these, even the casual dress nights. ...... Nei.