My brother updated his iPod today but because he connected with my Apple ID, he is receiving all my iMessages and FaceTime calls on his iPod.
How do I stop this from happening?
You can simple switch of these sync settings by disabling the services in the Settings < FaceTime/Messages.
Of course, if you've got like a troll brother, he will simply turn back on these services. If that's the case, you can protect these settings with Restrictions. At least, you can for FaceTime. With a simple password, you can prevent him from using FaceTime.
If you let him use your Apple ID, he should be able to live with the fact his iPod is password protected.
Or you can make him his own Apple ID of course. It's free of charge and done within a few clicks.
If he uses your Apple ID in order to use iTunes Match or get the apps you've bought, that's possible as well. Please see this extensive topic about sharing an Apple ID.