So you want to connect the displays to the Arduino board ?
Which Arduino board do you have ?
I would like to use the normal serial connection (via the usb) for uploading the sketch and for the serial monitor of the Arduino IDE.
You need (a few) extra serial ports.
The Arduino Mega has 3 extra serial ports.
The Arduino Leonardo has 1 extra serial ports.
The Arduino Uno has no extra serial ports.
The SoftwareSerial library is included in the Arduino software. http://arduino.cc/en/Reference/SoftwareSerial
You can use it to create more serial ports. So you still will be able to connect a few displays to the Arduino Uno for example.
Next step: connect the display to the Arduino.
If you could make the serial communication TTL level, that would make things a lot easier. Normally connect RX to TX and TX to RX. But sometimes the signal is inverted.
The SoftwareSerial has a (undocumented) feature for inverted serial data.
If you want to connect the higher voltage 'real' RS232 signal to the Arduino, you need a RS232 converter board. Most of them have a MAX232 or MAX2323 chip.http://www.ebay.com/sch/i.html?LH_BIN=1&_sop=15&_osacat=0&_from=R40&LH_PrefLoc=2&_nkw=rs232+ttl+-usb+module+-mini&_sacat=0
You won't have any trouble with inverted serial data with those converter boards, but they still could have the label "RX" for RX or TX and "TX" could be TX or RX. So you still have to try and see what works.
Or ... Do you you want to control the displays with an Arduino, while the displays are connected to the PC ?
Could you make a drawing of what you want. I still don't understand it.