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Interesting question!

You could hollow out oranges and make a variation on the blood orange jelly smiles:
http://www.thekitchn.com/thekitchn/tips-techniques/gallery-how-to-make-blood-orange-jelly-smiles-074678

Humbow is always delicious (a Chinese dumpling filled with BBQ pork). I can’t recommend a specific recipe but here’s a pic:
http://allrecipes.com/Recipe/Chinese-Steamed-Buns-With-BBQ-Pork-Filling/Detail.aspx

Gougeres if you can use an oven and serve them hot:
http://www.doriegreenspan.com/print/2008/11/all-things-considered-considers-cream-puffs.html

And one of my absolute favorites and a huge crown pleaser among olive-loves, cheddar olives:
http://www.thekitchn.com/thekitchn/hors-doeuvres/recipe-cheddar-olives-047009

Buckeyes: the classic smash hit of any party.
http://allrecipes.com/recipe/buckeyes-i/Detail.aspx

Sounds like a fun party! Cherry peppers (Peppadew in jars?) are pretty round... I'd stuff them with some cooling cream cheese with some herbs mixed in.
Round fruits (cherries/grapes etc) dipped in chocolate - if it was some kind of sports ball you're aiming for, a bit of white chocolate piping could give it the football/tennis ball look?
You could always make a round English Christmas pudding (and then flambe it - surely there are bonus points for setting things on fire?!)or a scottish clootie dumpling - it's boiled in a muslin so comes up pretty round (although I can't vouch for a clootie's flavour!)

You could make some arancini with various cheeses in the middle.

Snowman poop!

1 pack of Oreos (buzzed until turned to powder) mixed with 1 package (8 oz) of cream cheese (softened). Form into balls and freeze for about 15 min to 30 min. Using tooth picks or chopsticks (or whatever's easiest for you), coat the balls with melted white chocolate chips and refrigerate. (The whole process is easier if you freeze the balls and refrigerate after dipping by placing them on a cookie sheet or a jelly roll pan lined with wax paper.)

If you use regular chocolate chips it'll be reindeer poop, but that's trickier since it stays pretty thick when melted, and you can't microwave it too many times or it'll burn. The white chocolate chips are runnier when hot and don't burn as easily.

Round port wine jello shots. We made these for a party once, and they went over very well. I don't exactly have a recipe--get several packets of gelatin, dissolve in a small amount of hot port, add more port, add sugar to taste, let set. We did ours in a round ice-cube tray so they were these beautiful balls of different colors of purple and amber (we did tawny, ruby, and madeira). They were so weird--we didn't expect anyone to like them--but they all got eaten, and a good time was had by all.

Also, these links might help you brain storm:

http://chowhound.chow.com/topics/566541

http://answers.yahoo.com/question/index?qid=20070621070526AAM1uHW

http://foodstorm.blogspot.com/2006/04/round-food.html
(This doesn't really give ideas other than to shape non-round foods into a round shape—like scrambled eggs in a round mold.)

Definitely Peanut Butter Balls!! http://allrecipes.com/Recipe/Peanut-Butter-Balls-III/Detail.aspx

Or Cake Balls. Check out Bakerella.com for a ton of cute ideas on the cake ball / cake pop variations.

Chocolate and Pop Rocks Lollipop.

Check out the Voltaggio Brothers in this video, but get some round lollipop molds. Here is their Chocolate Tempering for the At-Home Chef post as well.

Marinated mini mozzerella balls are always delicious!!!

Marinated labneh balls with nice bread or melba toast (my favorite).

Left-field perhaps, but how about this salad:

http://www.britishlarder.co.uk/maple-glazed-parsnip-and-israeli-couscous-salad/

Truffles for dessert, of course!

Tea eggs. Hard boil some small or medium eggs, cool, crack the shell all over with the back of a spoon, soak in a mixture of strong tea, soy, star anise. Peel [they should look like faux marble] and serve with some Asian dipping sauce or a dry dip - mixture of salt, Sezhuan pepper, and a pinch of sugar.

Sausage balls! You can make them in advance and freeze them!

http://allrecipes.com/Recipe/Sausage-Balls-2/Detail.aspx

Fried goat cheese balls are divine!

I think, as a joke, you should go low-tech and bring a box of munchkins.

I'd go for arancini, with something hidden inside, roasted pepper or a piece of soft mozzarella. If you make the risotto vegetarian it's a more versatile dish in a mixed group of diners.

Another thought is to make miniature meatballs and serve them in lettuce cups with a sauce. Think a pork meatball, or gardein if you're vegetarian, and accompanied by fried noodles and a spicy Thai sauce. Just use a truffle scoop to make the meatballs quickly.

If you want dessert, truffles are pretty easy, if you want to go all out then pipe the truffle mixture into a raspberry and then encase the raspberry in truffle mixture and shape into a ball, dip those in tempered chocolate. Another dessert idea, fried truffles, Michel Richart offered a recipe for those in Baking with Julia or in her Master Chefs book. The truffles are frozen, breaded, fried, and it's a hot/cold combination that's really unforgettable. Or try the recipe here for black sesame truffles:

http://sweetpleasure.blogspot.com/2006_11_01_archive.html

How about rellenos de papa?

Or an asian variation on the rice balls, stuffed with salmon, umeboshi, or tuna. And sprinkled with furikake!

Chocolate dipped marshmallows rolled in graham cracker crumbs...smores on a stick.

Make Gold-Dusted Bourbon Pecan Balls but add silver luster dust to the coating as well so they shimmer and shine like disco balls:

http://www.epicurious.com/recipes/food/views/Gold-Dusted-Bourbon-Pecan-Balls-13463

http://www.foodnetwork.com/recipes/paula-deen/hushpuppies-recipe/index.html

I love hushpuppies! And I recommend serving them with a honey-mustard sauce. It's so delicious!

Believe it or not there is actually a cookbook devoted to this called Balls! by Angela Murrills. My brother got it for me for Christmas last year. It's full of all sorts of tasty things in ball form.

http://www.foodchannel.com/recipes/1766-fried-risotto-balls

Just make up some risotto and follow the instructions. I made this with a mushroom and asparagus risotto, but with goat cheese in the middle instead of mozza. It remains one of the most amazing things I've ever tasted.

there was an outrageous episode of iron chef where paula deen made fudge balls using processed cheese... that should at least get you some attention!

http://www.foodnetwork.com/recipes/paula-deen/chocolate-cheese-fudge-recipe/index.html

Speaking of Paula Deen, she also had a recipe for Fried Butter Balls. Seriously.

http://www.foodnetwork.com/recipes/paula-deen/paulas-fried-butter-balls-recipe/index.html

Wow! So many great ideas...thank you! The party is on January 30th and I'm looking forward to it.

I will go through all of the links and choose a couple of options to bring to the party. I will post my choices and some pictures of the party on my blog, photospoetryprose.com if anyone is interested.

Thanks again to the readers and to the kitchn for the help!

sorry...photospoetryprose.blogspot.com.

for some reason, I'm having issues with my profile/username.

I think you should make Ice Planets, from the tv show Firefly. I don't think there's a specific recipe, but I'm assuming it's supposed to be ice cream. Basically they're some sort of round food about the size of a baseball hung by a string from a stick, and you have to try to eat them hanging like that. Also, this would immediately boost your geek cred in the right crowd.

River: "My food is problematic."

Here's a link to a fun recipe: http://tastyplanner.com/blog/articles/The-Problem-with-Ice-Planets

CHEESE BALLS! The ultimate party food.

I like Amy Sedaris. I like Amy Sedaris' cheeseball recipes.

I second the marinated labneh balls. They are delicious. I make them from a recipe on Leite's Culinaria:

http://leitesculinaria.com/2278/recipes-yogurt-cheese-balls-garlic-dill-oil-aleppo-pepper.html

I also like two more ball shaped recipes on Leite's: the curried chicken rolled in toasted coconut and the mini lamb meatballs:

http://leitesculinaria.com/863/recipes-curried-chicken-rolled-in-toasted-coconut.html

http://leitesculinaria.com/952/recipes-lamb-meatballs-with-yogurt-sauce.html

Stick any leftover lamb meatballs and labneh balls together in a pita and best sandwich ever!