I'd say immunity takes precedence over vulnerability, or susceptibility for that matter. Therefore in a similar case, a Lawful Good Balor (w/ Chaotic and Evil subtypes) would be completely immune to blasphemy/dictum/holy word/word of chaos chain since those spell only affect creatures that are non-[alignment] creatures.

However, the wording of Holy Aura/Unholy Aura chain doesn't seem to rule out that good/evil creatures are immune to the secondary effect (holy word's blinding effect for example), only that it targets an opposed alignment. Since our balor (and the HW) do possess both good and evil nature, they'd be susceptible (but not immune) to the effects of those aura-like spells.