You would need a 4053 for every 3 servo channels (
3PDT).
To "switch" it, it needs to be a logic hi/low, not PWM. If all you have available is a PWM signal, you could probably use a uC to determine the length of the pulse, and set the logic IO accordingly.
You do need a cable, yes. USB will not work; you need RS232. If your computer doesn't have an RS232 port, you can get a USB > RS232 adapter.
I suggest you look at the cable options SFE has to offer:
Official PICAXE USB programming cable, if you want the official USB cable.
RS232 cable, if you have an RS232 port, or a USB > RS232 adapter (with DB9 connection).
SFE PICAXE USB programming adapter, if you want the cheaper of the USB options. You will also need a
USB mini cable, and a
3.5mm - 3.5mm stereo cable.
For the serial to breadboard connection, I suggest using an
audio jack and the matching
breadboard breakout.
If you don't have an RS232 port, the cheapest programming option would be to get an inexpensive (though decent) USB > RS232 adapter from someplace like ebay, and then hack an old RS232 cable for connection to the breadboard.
Thanks for the link to the topic about PICAXE interrupts, I will definitely read that again.
Since I made that PICAXE based servo controller, I have started using Arduino a lot. I haven't used it with servos yet, but I have used it as an NXT I2C slave device. I think Arduino might be the way to go. It's fairly in-expensive (you can buy a mock nano on eBay for $15, and the nano has USB > serial on-board), and it is really easy to use. Using the Arduino, you could read the length of a PWM pulse, so you know the state of the toggle switch.