Three UART connections to an ATMega328?

There is only one UART on the 328P. If your bandwidth is low you can do software emulation of a UART with some of the other digital pins. There is an Arduino library called NewSoftSerial that enables this functionality.

If you don't have enough hardware serial ports, you can use other IO pins for serial under software control. But, don't expect to get 115200bps...

http://arduiniana.org/libraries/NewSoftSerial/

It is true - only one serial port on the ATMega 328. You can do what the others suggested and use software-serial or you can use a multiplexer if you don't need your serial ports to be always on. Sparkfun has one that can be used for 3.3V here: http://www.sparkfun.com/commerce/product_info.php?products_id=8970

Basically, if there isn't constant traffic, especially if you only need to send messages or you will only receive one response for one command then you can use the multiplexer. Just switch to the device you want, send commands, wait for response, then switch to another device.