The "omni" wheels are indeed just like a castor, but they are more stable with side loads then the shopping cart variety. They allow you to turn about the center of your drive wheels. DO NOT try to power them, because they do not operate well in that manner.
If you are looking to go forward, back, sideways and round and round, look into Mechanum wheels.
Here is an example of them in an industrial application:
http://www.youtube.com/watch?v=CjcyHicm3NA
AndyMark sells a 6" and an 8" version as well.
There are some issues with them, such as a certain level of finesse needed in the coding of the robot and each wheel needs individual power in order for them to operate properly. They also do not do well when one of the wheels is lifted off the ground. You may also want to look into using a gyro to maintain a certain orientation of the robot as well.
Hope this all helps and good luck with the rest of build season.