I’m not sure about parables in particular, but he used rhetoric and other conventions that would be understood by whichever audience he was addressing. In Athens, he quoted Greek poet Epimenides, and the work ‘Phaenomena’ by Greek poet Aratus while he was witnessing on Mars Hill to the Epicureans and Stoics. Elsewhere in 1 Cor and Titus, he also quoted Greek poetry. He made use of fitting devices in his ministry to try to reach out to the various groups he was in contact with.
For whereas I was free as to all, I made myself the servant of all, that I might gain the more. And I became to the Jews, a Jew, that I might gain the Jews:It is no glory: That is, I have nothing to glory of. To them that are under the law, as if I were under the law, (whereas myself was not under the law,) that I might gain them that were under the law. To them that were without the law, as if I were without the law, (whereas I was not without the law of God, but was in the law of Christ,) that I might gain them that were without the law. To the weak I became weak, that I might gain the weak. I became all things to all men, that I might save all. And I do all things for the gospel’ s sake: that I may be made partaker thereof.(1 Cor 9:19-23)