There are lots of Asian foods served on a stick. Thai or Indonesian satays and Japanese yakitori are the first to come to mind. For keeping within a budget, yakitori is great, since it tastes better with chicken thighs than breasts. That keeps things really cheap, as long as you're not attached to using organic, free-range chicken.
For yakitori, take 2 parts soya sauce, 2 parts mirin, 1 part sake, 1 part sugar and a little garlic and fresh ginger. Simmer until the sugar has dissolved. Thicken slightly with a slurry of equal parts cornstarch and water. (Use about one tablespoon of cornstarch to thicken about 1 cup of yakitori glaze.)
Cube some boneless chicken thighs and thread them onto bamboo skewers that have been soaked in water for half an hour, alternating with pieces of green onion. Grill them until cooked through. Towards the end of the cooking time, brush them with the glaze. If you start brushing the glaze on too early, it will burn and taste awful, so be careful!
These are also good for a party because they don't have to be served right off the grill, they can cool down a little. Just be sure to keep them warm so you don't give your guests food poisoning.
Another item you may want to look into, if you like Japanese food in general and miso in particular, is dengaku