Ooh, how fun! what a great theme. I remember DD watching Elmo's World, didn't he start off by saying "Hi everybody" ? You could do your own invitations and start them off like that maybe? "Hi everybody... xxxx is having an Elmo party"
If invites are for kids and parents, you could address it to the kids and add that big monsters are welcome too? or vice versa?

Maybe draw or paint a pic of Elmo's face, along with a seperate piece for his nose and play "Pin the nose on Elmo" If you were going to play a game like that?

Print off some pictures of Elmo for the kids to colour in? something fun to do.

I think Wilton do a Elmo cake tin, it's of his face. Ebay, or try spotlight, I've seen wilton tins in there too.

If you don't want to get plates and cups etc, with elmo all over them, just buy things in Elmo colours....red cups, yellow napkins, plates, balloons, streamers..etc.. If you were able to get elmo stickers you could stick them on some plastic cups for the kids?

Do a banner up to say "Elmo is soo happy to see you" instead of happy birthday! or add it to an invite to say, Elmo and xxxx will be so happy to see you at xxxx's birthday party..

Will try to think of some more things and come back later typing one handed with DS is proving to be a little difficult at the moment lol!