The first allusion is to Epimenides the Cretan, the poet Paul cited in Titus 1:12. The original poem no longer exists, but fragments appear in other ancient writers. The second citation is from Aratus, a Cilcian poet (Phaenomena 5). The original line, “in him we move and live and have our being,” was pantheistic, but Paul spins this line into a statement about God as the source of our life.
In other words, he ignores the writer’s original intention so that he can effective make his point. If Aratus had been in the audience in Acts 17, what would he have said in response to Paul? In modern scholarly writing, misrepresenting another scholar’s ideas is not just a mistake, but intellectual dishonesty. Someone who does this sort of thing today would be dismissed as a poor scholar or a crank (or possibly just a biblio-blogger). In some areas of scholarship, authorial intent is not important, so perhaps Paul is not out of line here. Can Paul legitimately pull this line out of context and reapply it to prove the God of the Bible is superior to the other gods?
While I do not think this kind of cultural education is a bad idea at all, that may not be Paul’s point in using these sources (or, Luke’s point in presenting Paul as using these sources). These lines may have been well known proverbial wisdom, common knowledge. If so, then the allusion to Greek poets is more like the preacher who uses a common phrase in order to make his point.
Or better, this is an example of a modern pastor quoting lyrics of popular songs to make a point. I occasionally use a line from a popular movie or song in order to make a point (although with my taste in music, it usually does not work very well). This comes down to knowing your audience. I have found that I can get a lot further with college age group with a Simpsons reference, while the same line is lost on an adult group. Perhaps that is what Paul is doing here in Acts 17 – he is riffing on the culture.
In both of the allusions Paul simply intends to demonstrate his thinking is not too far from the culture the audience understood and appreciated. To cite the Hebrew Bible would have been fruitless since the audience did not know it, nor were they inclined to listen to philosophy drawn Jewish texts.
If the message of the Gospel is obscured by the using Fifty Shades of Grey as a sermon title, or by playing U2 songs during your worship, or hosting a Dancing with the Stars night at church, then you have missed Paul’s point in Acts 17.