Hi Tracy,
Sorry I've taken so long to answer but I wanted to give you a link on the US site and it wasn't working for UK guests for a while, it's working now though but you may need to click the "visit US Site" link on the left hand side at the top of the UK site :-)
Anyway, thanks so much for all the questions, I hope I'm helping. How exciting that it's your first trip to Disney World and 3 birthdays too. Of course you can celebrate your childrens birthdays late, the only thing they won't be able to participate in is the free park tickets, fun card etc because you're not there on their actual day. When you check into your resort tell them you're celebrating and they will give you Birthday badges for your children to wear, also note it on any dining reservations. You may also want to order a cake or some other special treat for them, here's a link
HERE (hope it works for you) with some fun ideas. They really vary in price but hopefully it will give you some ideas, if you have girls the Bibbidi Bobbidi Boutique is great fun or for boys how about the archery!
As always if you have anymore questions please ask, I'm here to help!
Jo