On the cruise, you will have 2 luggage tags per passenger for checked luggage, and each passenger is also allowed one carry-on bag and one personal item (such as a diaper bag, purse, or backpack). I don’t know what happens if you exceed 4 items per person, but since porters at the cruise terminal have additional luggage tags, I do not think anyone actually counts bags.
Airlines are different. They typically have the same limits (or may allow only 1 checked bag without a fee) and they do pay attention and will charge for excessive bags. Strollers do not count toward the limit on most airlines, but I don’t know if boxes would — my guess is yes, because the check-in clerk won’t know what’s in a sealed box. As mentioned above, check with your airline.