A ray spell can crit and deal double damage, because the spell is an "Effect: Ray" and so the ray itself is the "weapon" damage which is the only kind of extra dice you multiply on a crit. The claws of the beast power itself cannot crit, because the power targets you; you are not attacking with the power, you are attacking with your natural weapon which happens to be modified by the power. However, if you crit with a natural weapon, you multiply your weapon damage, and the claws of the beast specifically deal the Xd4 damage as their weapon damage, and so it is multiplied on a crit. Contrast this with the claw of energy power that adds extra damage to an existing natural weapon, or sneak attack which adds precision damage to any attack, which isn't multiplied
So: Crit with a ray that does damage, multiply that damage; deal sneak attack with that ray, don't multiply the SA damage. Crit with a claw attack with claws of the beast active, multiply the CotB damage; crit with a claw attack with claw of energy active, don't multiply the CoE damage.