So, here is my balancing attempt.
Haug, paragraph 2:
In addition, you can invoke the rune as a bonus action, gaining resistance to all damage until the end of your next turn. Once you invoke the rune, you can’t do so again until you finish a short or long rest.
Uvar, paragraph 2:
In addition, you can invoke the rune as a bonus action to enter a prophetic state for 1 minute or until you’re
incapacitated. Until the state ends, when you or another creature you can see within 60 feet of you makes an attack roll, a saving throw, or an ability check, you can use your reaction to cause the roll to have
advantage or
disadvantage. You can do this once for each of attack rolls, saving throws and ability checks until the prophetic state ends. Once you invoke the rune, you can’t do so again until you finish a short or long rest.
That weakens the two strongest runes, but not in a crippling way. Haug works on any damage, but only for 1 round; Uvar lets you impose advantage or disadvantage on 3 different rolls in a minute, but not repeatedly.
I might make Ild stronger:
In addition, as a bonus action you can surround a weapon with a fiery aura. Once per turn when you hit a creature with a weapon attack, the target must succeed on a Strength saving throw or the fiery aura transforms into shackles and
restraines the creature for 1 minute. While
restrained by the shackles, the target takes 2d6 fire damage at the start of each of its turns. The target can repeat the saving throw at the end of each of its turns, banishing the shackles on a success. The fiery aura emits dim light in a 10' radius, and lasts until a creature fails a saving throw against it, or 1 minute passes. Once you invoke the rune, you can’t do so again until you finish a short or long rest.
That might be a bit strong; with this rewording, you can force 1 save/round until someone fails it.
The original version was a bit "ok, make a saving throw... nothing happened. See you next short rest!" to much for me.