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Does psychic power strength modifications work against Monolith? Sanguine sword as example

Yes, the same way a Power Fist works against a Monolith.

A Libby who has used Sanguine Sword is S10 and gets to use that Strength against the Lith.

Ok.
Just the part "In practice, any weapon attacking the Monolith will roll for Armor Penetration using it's unaugmented strength and a single D6 no matter what" made me think librarian would still have to use S4.
Unaugmented is not the same thing as unmodified?

The librarians strength is modified, but the Sanguine Sword, and the weapon he is hitting with, isnt modified.

Sanguine sword is not a weapon itself. It just modifies librarians strength for closecombat attacks.

Which is why "and the weapon he is hitting with" was in there.

ok. got your point now.