Below is the Bestiary 6 description of the Animus Shade's Mental Schism ability. Looking for confirmation that this ability results in this particular evil undead being unaffected by a Paladin or celestial's Smite Evil because Smite Evil is alignment based.
Mental Schism (Su): An animus shade’s
mind is a chaotic tangle of shredded
remnants of the dominant personality
that once subsumed it. This mercurial
state of being is too piecemeal for
alignment-based effects to take hold.
The animus shade is immune to all
effects that are dependent on alignment.
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Yes it would be immune to Smite Evil, as that is the definitive effect dependent on alignment. Also spells like protection from evil, holy smite, and so forth would not work. Spell that specifically target Undead should work fine, as long as they do not reference alignment.
Paladin abilities that do not reference evil should work fine, an Iroran Paladin's Personal Trial would work, even though it replaces Smite Evil.