Finding fights for BlazBlue as a whole is very tricky because in quite a few of the tiers they occupy they outhax most if not all of them (I think it was stated that the strongest Low 5-B on the site was either Susano'o if speed was equalized and Ragna if it was unequalized). I guess Reinhard vs Susano'o would be an interesting fight but he's 5-B and has 1-A hax while still being said tier.
Sorry for taking so long to respond, college has been quite busy. XD
Izayoi is the prototype of what went on to be the Murakumo Units and her purpose is to kill Observers. Izayoi can use an ability called the Immortal Breaker which can kill any being outside of reason (basically any immortal). The only thing that can stop the Immortal Breaker is the Power of Order, as the ability was used on Jin, and Izayoi's blade didn't pierce him and Izanami isn't affected by it due to her being death itself.
Izayoi is just as capable as the Murakumo's in strength and agility and can neutralize Phenomena Intervention from Observers as her function as the Izayoi.
Hax = Killing immortals and/or beings out of reason, can nullify Phenomena Intervention (reality warping). She has some Power of Order of her own due to Tsubaki having some of it, but it's not Hakumen strong and no where near Jin strong.
I don't know any particular immunities and or resistances, but I assume she has some resistance to Phenomena Intervention/Reality Warping due to 1. The Power of Order and 2. Her function as the Izayoi.
She has shown mind resistance as she was able to break free from Izanami's control in Chrono Phantasma (though she did have help from Jin) and I think she had some recollection of what happened in Chrono Phantasma while in the Embryo due to the Power of Order (though no where near the extension of Jin who remembers everything).
In fact, due to the Power of Order, most of the hax Jin and Hakumen have thanks to it should apply to her, just not as strong as those two (same with Makoto who also has the Power of Order).
Valkenhayn is a master of martial arts and close combat to the point where he fought the Black Beast bare handed and completely unarmed. The reason why he was able to harm the Black Beast is because like the Beast, he is a being that exists outside of logic. Valkenhayn can also teleport and can obviously turn into a wolf but can control how much; either partially (like during gameplay where he can change his limbs into wolf limbs) or completely into a wolf (his drive or during his Astral).
Trinity is incredibly adept at magic, especially defensive or barrier, to the possibility to be better at it then Nine. Trinity also has powerful reinforcing magic: In Phase 0, she tore gigantic boulders with her bare hands and in Phase Shift 1, she took a powerful blast of magic to the face and only suffered a mild concussion. Trinity's biggest feat was the ability to materialize Terumi through a time paradox using the Muchorin and Jubei's help.
Nine, like Trinity, is indredibly adept at magic and was the creator of all the Nox Nyctores. She has all kinds of sorcery at her disposal like Gravity Seed, Mind Eater, Infinite Corridors, Teleportation and Infinite Gravity, her own spell, which was used as a catalyst for creating the Nox Nyctores for having the ability to compress and sealing the soul of the Black Beast. Kokonoe also used it on a Black Beast to stop it from destroying Sector 7.
Jubei is considered by many, including Hakumen and Terumi, to be the strongest warrior alive and was claimed to be undefeated in a one on one fight. His eye under the patch, which was from his brother Tomomori, has the ability called Sekigan, which can allow the true form of whatever it sees to materialize (he used it to expose Terumi to Hakumen so he can seal him). Jubei also holds the Mucro Somnio: Musashi, a Nox Nyctores that destroys anything it can cut, as proven when he manages to open Nine's barrier around the Requiem with the Musashi.
I don't particularly know because I don't think they are resistant to one thing or most things in particular. I mean they themselves are resistant by their own defenses, but I don't seem to recall a particular thing they're immune to and resistant to.