Let me see if I can summarize what we have so far in the comments above.
We have perhaps three views inside of wrong view (if we use the full sentences in the Access To Insight version as breaks between views). These are:
(1) There is nothing given, nothing offered, nothing sacrificed.
(2) There is no fruit or result of good or bad actions.
(3) There is no this world, no next world, no mother, no father, no spontaneously reborn beings; no priests or contemplatives who, faring rightly & practicing rightly, proclaim this world & the next after having directly known & realized it for themselves.
Theory-wise we have:
(A) That (1) and (2) are the views of Purana Kassapa, possibly addressing both the Brahminical view of kamma and the heretical view.
(B) That all three are nihilist views
(C ) That all three are Ajita Kesakambali's materialist views (though I think the phrasing was borrowed)
And notes on possible meanings include:
(1) There is no (gain from making) gifts, offerings, sacrifice
(2) There is no fruition, no ripening of good and bad deeds
(3) This world and the other world do not exist; there is no (benefit from duties towards) mother and father; there are not beings of spontaneous birth; there are not to be found in the world ascetics and brahmins who, living and practicing rightly, proclaim (the existence of) both this world and the next, having personally experienced them by superior knowledge.
(3) That the mother/father phrase is about the value of honoring mother and father (not a flat denial that they exist).
(0) That taken as a whole, it is simply the reverse of mundane right view, contrasting a person with morals with one who does not.
(3) That “spontaneously born beings” refers to devas
(3) That “this world and next” has to do with “this life and the next” (but I'd say that that is stretching the point).
(3) That “this world and the next” is literal but no materialist schools denied this world (I think that's more evidence that Ajita's block of text in the DN was borrowed from this sutta without good understanding of the differences in the schools).
Next up, I will attempt to pull a rabbit out of a hat.