Hi Nikkima, I am not sure about a birthday party or that sort of thing, but you can arrange a birthday surprise at a Character Meal, which you would reseve in advance. YOu can get your DS a button to wear for the whole trip that says something like, "Birthday Boy" or " I'm Four" or along that lines. You get the button from Guest Services in the parks. But check with your resort, if you stay on property. We got our "First Trip" buttons at the hotel, without even asking for them!
As for meeting the characters, the best way is the Character Meals, so you are guaranteed to meet certain ones. Like a meal at Crystal Palace means you meet Winnie, Tigger, Eeyore etc... We had lunch there and it was great! Breakfast at Ohana, at the Poly was wonderful and it was to meet Lilo and Stich, but Mickey and Pluto were there to!
You can always check out the Disney website for the schedule of when and were the other characters will be in the parks for a certain day. This will help you plan your day.
Hope this helps and have a super time!!
Suz