Yes you can in a 'reasonable' amount. A case of soda is often passed through without comment but I would only recommend a sixpack or two unless you are a very heavy soda drinker.
For water, don;t bother. Bring on a couple of bottles or maybe even a sixpack if you wish and just refill the bottles onboard from the tap or from the dispenser on the Lido deck. It is probably as pure or even purer than bottled water.
a couple of six-packsof soda is ok. As for water, do what we do. Each person has their own carry-on sports bottle, filled with water - they aren't going to take a bottle of water that you are drinking from away from you. Then we pack a couple extra empty sportsbottles in our luggage --fill them when you get to your stateroom and put them in the frige. The ships water is very good quality, very pure.