If someone played Vengeance for Elia against me, can I play my Vengeance for Elia for redirect claim once again to the original defender?

No. Being chosen to satisfy claim for a challenge does not change who was actually the defender and attacker.

For example, a defending Martell player could choose to use both VfE and also Ghaston Grey.

For example, a defending Martell player could choose to use both VfE and also Ghaston Grey.

Text on the card is:

" Interrupt : When claim is applied for a challenge in which you are the defending player, choose an opponent. That player must satisfy the normal claim effect instead of you as if he or she were the defending player."

As Grimwalker says, the thing to notice here is that the target opponent does not actually become the defending player. He only satisfies the claim effect as if he or she had been. Since the target of VfE is only treated as the defending player when satisfying claim, they cannot trigger Interrupts to applying claim effects (such as VfE) as the "defending player" because Interrupts are always triggered before the thing that they are interrupting happens.

So, as Grimwalker described, the person targeted by VfE cannot answer with a VfE of their own because, since they are not the actual defending player, they can never meet the play restriction of "...a challenge in which you are the defending player...".

Yup. I started typing that the Case with Ghaston Grey is obvious.

And how about Vengeance for Elia vs Calm over Westeros?

If my active plot is the Calm over Westeros and I get hit back with Vengeance for Elia (and challenge type matches my choice with CoW), do I reduce claim value of my plot card? I assume the answer is no, because I am not the actual defending player in this challenge. (On CoW there is also a text "during challenges of that type in which you are the defending player")

The lasting effect of Calm Over Westeros applies to modify the circumstances when you satisfy claim. As such, it would apply in the same moment in which the player chosen for VfE is being treated as the "defending player" and would lower claim.

The other side of that is if the player who played VfE has CoW revealed, their plot would not benefit the event's target player who is satisfying claim.

Here's how it breaks down:

A. "Apply Claim Result" window reached (flowchart window 4.2.4)

B. "Apply Claim Result" window is interrupted by VfE, played by defending player.

C. "Apply Claim Result" window is resolved (i.e., claim satisfied) with target player from B acting as "defending player"

D. "Apply Claim Result" window is reacted to.

VfE only changes the "identity" of the "defending player" during C. So the target chosen in B could not play their own VfE (which would be triggered in B, where they are not considered the "defending player"), but could apply the effects of CoW (which is applied in C, where they are considered to be the "defending player").

OK. Thanks for answer.