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Say you have a rune priest with a wolf tail talisman as well as an allied witch hunter inquisitor lord with a psychic hood. Your opponent casts a psychic power on your rune priests unit. Can you use the runic weapon to try and stop the power and if that fails use the hood and if that fails use the talisman? If so is there a specific order they should be used in?

Yes, and the Talisman is used last
The order does not matter, particularly...

Agreed, I'm a little skeptical about the hood and the Runic Weapon stacking however, since they are essentially the same check in a different form, but I know that the Runic Weapon and the Wolf Tail Talisman would stack due to when each check occurs.

Except they arent the same check - the Runic weapon is considerably better than a Ld10 hood vs a LD10 opponent (although worse against Ld9 or less, but not many of those!) and is resolved in a different way.