The essential idea of cultismo is classicism, in the sense of words and expressions, and by extension modes of thought, derived from Greek and Latin antiquity. It has positive connotations of the learned and erudite, and potential negative connotations of the affected, the pretentious, the pedantic.

In your first context, I think it has this basic meaning of learned classical words and expressions: Latinisms or Hellenisms. Los cultismos de la poesía refers to this type of language used in poetry.

This type of word or expression can be called a classicism, one of whose definitions is:

- "A Greek or Latin expression or idiom" (American Heritage)
- "a. a Greek or Latin form or expression
b. an expression in a modern language, such as English, that is modelled on a Greek or Latin form" (Collins)
- "a Greek or Latin idiom or form, esp. one used in some other language" (Random House)
- "a classical idiom or expression" (Merriam-Webster)
etc.

However, in the second and third passages "cultismo(s)" is clearly being used in a pejorative sense. That sense is not affectedness or pedantry, however. "Cultismo" here clearly denotes something morally suspect, potentially blameworthy. To understand this requires some cultural background. The extreme idealisation and emulation of the classical (Greco-Latin) world that characterised the European Renaissance aroused a certain measure of suspicion and condemnation in the Catholic Church, or at least certain sections of it, because it implied devotion to a non-Christian culture, ultimately a pagan culture. Thus there was a curious mixture of veneration for classical literature and suspicion, in some quarters, that this veneration could become idolatrous.

That is the sense in which "cultismo" is being used in passages 2 and 3. I don't think that it is purely a matter of language in these contexts; it refers more broadly to classical culture, classicism. But since the connotations of classicism in English are almost entirely positive, I think it would be helpful to make the point I've been outlining explicit by saying "pagan classicism" in these cases.

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Note added at 4 hrs (2015-10-22 02:18:16 GMT)
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To the more narrow-minded kind of theologian poetic metaphors are seductive distractions and classical myths are the doings of false gods.

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Note added at 8 hrs (2015-10-22 06:14:15 GMT)
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I agree with you that "cultismo" is unlikely to refer to what is properly and normally called "culteranismo" these days (that is, the specific poetic style of Góngora and his followers, anticipated by Luis Carrillo y Sotomayor). It is true that Sor Juana's poetry displays features of that style, but I don't think it's what passage 3 is referring to.