Welcome aboard, Kali! This must be your first Disney cruise, so I'm sure you're anxious to get onboard and begin the fun!
You didn't mention which cruise you were taking, so I can't tell you exactly which themed nights you will have, but you can certainly expect a few nights of Cruise Casual attire. For the men and boys this would include collared shirts (even polos are fine) and long pants. Though, use your best judgement with little boys. I've let my son wear nice shorts with a polo to dinner on Cruise Casual nights, and have seen many others doing the same. If you're on a six-night or longer cruise, you'll have both a Formal Night and a Semi-Formal Night. On shorter cruises, expect just the Semi-Formal or optional dress-up night.
Then, of course, Disney Cruise Line's most popular night is Pirate Night. Check out Disney Cruise Line's website for the fun events during the
Pirates IN the Caribbean Deck Party that takes place on most sailings. Be sure to pack a pirate outfit or accessory for each of your family members so you can really experience the fun! If you don't have a closet full of pirate gear waiting to go, don't worry! The shops onboard will offer a variety of pirate costumes and accessories, so you won't be left out! On Pirate Night, expect to see anything from a simple pirate bandana to folks whose entire families are head to toe in pirate costumes. It's a really fun evening!
I hope this helps you to plan your outfits. Have a great trip, Kali!