I've organized several tea parties for friend's and family birthdays this year and a couple of ideas that I came up with were inexpensive.
For a regular tea party with an English theme (our family are from England) I looked at English quizzes online and came up with questions and multiple choice answers. For instance, I'd copy a picture and give 3 possible answers of where it was, what year was the Queen's coronation and so on (number each question). I used masking tape to attach the questions on walls around the house. I handed out index cards for them to write the answers. It's also a good ice breaker for guests who don't know each other.
After everyone was settled, I read the answers and had a basket full of prizes. I found a lot of inexpensive English gifts from Marshalls and Ross and even Dollartree (English lavender soap) I wrapped each in tulle with a bow. The smaller prizes were a tea bag and English biscuit (cookie).
For another birthday (40th) I used index cards in two colors. On one I wrote questions such as what county was she born in, what was her first Halloween costume. I handed out two cards to each guest, one with the questions, the other had answers (and pictures) which they had to match up by swapping with other guests.