Can anyone tell me if powering my ATA + ROUTER + NAS + SWITCH + ADSL MODEM +22" LCD monitor from my PSU doable AND worth it?
Sure it's doable! Whether or not you survive the experiment remains to be seen, though...
No really, what I would do is this:
OK, so there would be actual wire stripping and binding involved.
#0) Do not kill or injure yourself!
If you're unsure of these things, don't mess with them.
#1) Examine each of your devices power label, wall-wart or brick supply and check its label: does it run on 5 or 12 volts? If yes, then it's easy to come by from your PSU. 7V can be managed as well, if tricky.
#2) Grab a kill-a-watt and measure the power draw of each device (using its stock power plug) to see if your PSU will be able to drive them. This is also determined by the rating of your PSU and the rest of the components in the pc.
#2a) My guess is, if all you want to run are desktop speakers and a home router, then yes there's no problem.
#2b) If you want to power a printer or separate laptop, too, that would probably be problematic, both in terms of odd voltages (not 5 or 12) and power draw (wattage).
#3) (For each device:)
#3a If you want to keep the stock power supplies intact: Buy appropriate cable and a matching power plug (the little one that goes into the device, not the wall plug).
#3b) If you are sure you won't be using the wall-warts: snip the power cable close to the brick to re-use as much cable as required.
#4) Pay attention to the polarity!
#5) Buy Molex (12V) Y-cables (easiest) or plugs and make your own (harder), and splice your devices in. It's probably best to have one Y-cable for each external device, though it will make a cable mess. Are you sure it'll be worth it?
#6) Plug in one device at a time, stick your fingers in your ears, close your eyes, and hit the power switch with a toe.
#7) Watch the fireworks, or smile at your success.
since all these 12V devices are quite far from my computer
Well, you should not snake a 5V cable across a room, let alone an entire flat. These things need to be close together (as you would a display or an external drive).