Asia covers a large area, so an Asian theme party could mean different things to different people. As such, if you're interested in throwing an oriental party theme, consider narrowing your scope to a particular theme, such as a geographical region, holiday, or tradition.
For example, there are many fine cuisines throughout Asia. China has multiple varieties, and that's just one (large) country. However, a Japanese sushi theme or Korean food approach may get you started on the right track.
Or maybe you're interested in throwing a party to celebrate the Chinese New Year. The point is to pick an idea and work your party around that.
For Asian party supplies, use the primary country/area as a guide. Colors of the flag are good, as are traditional colors of the region. If you are celebrating the Chinese New Year, consider bright colors such as red and yellow. Make some dragon masks out of card stock or poster board. Streamers are inexpensive and a fun way to create a festive atmosphere.
Use holiday lights around the room to represent fireworks. If you have posters from the region, hang those on the wall. Chinese lanterns are a fun and inexpensive way to add an "Asian" touch to any party.
Food options are many. Do some research on traditional foods from the area or for the specific celebration.
I recommend this Chinese recipe cookbook with over 500 delicious recipes.
Consider offering a variety of choices so your guests can sample the wonderful cuisines. Drinks will also vary by region, so look into this as well.
For the invitations, include the primary colors you plan to use and be sure to let your guests know the theme. If you wish them to dress a particular way, include this in the invitation so everyone will come prepared.
Because there are so many choices for an Asian theme party, you can make some basic preparations and decorations for many parties to come! Enjoy the learning process and taking a trip around the world from the comfort of your home.
Here is another variation, submitted by Robin from NY:
For my friend's birthday we hired a party coordinator and they designed a party package that was "A Trip to the Orient" party. It included red & black party goods, they used oriental fans and paper dragons to decorate the walls and hung paper lanterns from the ceiling. For entertainment, they arranged for the rental of Sumo wrestling suits and our guests "wrestled' each other for hours. It was great fun and a memorable party.