How exactly does Extort ability work?
From the text I would assume the following:

Whenever you cast a spell, if you pay {W/B} extra, then Extort ability will trigger.


That is incorrect. The triggering event is you cast a spell. Each time that event occurs, the ability triggers.
On resolution, you may pay {W/B} and cause life loss.

A player has 5 lands and 3 creatures with Extort ability. He then plays an Oblivion Ring for 3 mana ({2}{W}), so he now has 2 mana left. If he taps one, would all 3 Extorts trigger or just one?

All three trigger. Note that no time exists between Oblivion Ring being cast and Extort triggering. You don't have to option to tap anything then or when you place the ability on the stack.
When the third ability stacked resolves, you may pay {W/B}. If you do, each opponent loses 1 life and you gain that much life.
When the second ability stacked resolves, you may pay {W/B}. If you do, each opponent loses 1 life and you gain that much life.
When the first ability stacked resolves, you may pay {W/B}. If you do, each opponent loses 1 life and you gain that much life.
So you can cause each opponent to lose up to three life, but each life lost will cost you a mana.
Michael Snook explained how this isn't useless. This post is mostly about correcting your understanding of triggered abilities.