Lets say you just won a military challenge.

Can your oppenent play claim reversing events like Red Vengence before they have to claim? When does the window for responses for winning or losing a challenge open? If so isn't this where all other respones that key of off winning or losing a challegne like Price of War or Wintertime Maurdaures character ability happen?

According to my understand of the timing rules the response window for winning or losing a challenge only opens after claim happens. If this is true then cards like Red Vegence don't work. If I'm wrong they you can play cards like Price of War before your oppenent can claim possibile denying them saving cards when they have to claim.

Is any of this right or is there another explaination?

There is another explanation. Red Vengeance is a cancel and there is a specific spot for saves and cancels that happen during the resolution process.

I thought about that but I didn't know if it was a canel effect or not. So all the claim reversers has a cancel effect then?

Mallesh said:

If text of a response contains the word "cancel" or "save", then you know that it's a cancel or save response. (See CS rulebook). And such responses are played just before resolution of the effect you want to cancel/save from - in the case of Red Vengeance - before they have to claim, as you said.

Note that Martell player has still lost the challenge (only the claim effect was canceled) and other (normal) responses are played after claim, after power for unopposed, after renown and after passives.

Mallesh said:

Red Vengeance - Response: After you lose a challenge as the defender, kneel 2 influence to cancel the claim effect of that challenge. Then, choose an opponent to satisfy the claim of that challenge as if he or she had lost the challenge as the defender.

Rogue30 is right. You just look for the word "cancel" to determine whether or not something is a cancel effect. All the events like Red Vengeance, Misinformation, Feigned Retreat, etc. that change claim have the word "cancel," which is indeed what makes their timing work.