As a linguist, I can tell you a little about one word in particular: parthenios.

Parthenios roughly translates as "bastard," but more accurately as "son of an unmarried woman." It is formed off parthenos, a term typically used of a virgin, but better translated as "young woman." Anyway, parthenios shows up in Iliad 16 when Achilles is choosing whom to send with Patroklus into battle. Of the men he chooses, two are described as children of immortal fathers (Menesthios and Eudoros) but only one is labeled a parthenios (Eudoros). Both women are married at the time in our story, so the difference seems to be whether the sons were conceived in or out of wedlock, regardless of the father. Menesthios was called a son of Boros (much like Jesus is the son of Joseph) while Eudoros is a parthenios. Homer tells us that Ekhekles pays many bride-gifts to marry Eudoros's mother (16.190), so it seems that there wasn't a penalty for her lack of virginity. It may be, though, that so long as the sexual activity and birthing is kept secret, then there is no penalty (Hermes lies with her in secret and Eudoros is left to his grandfather to raise).

This latter explanation holds some weight because in Euripides's Ion, we find Kreousa raped and then birthing in secret, and when she exposes Ion to the elements, she retains the adjective parthenos. (Maybe someone else can talk about this example though. I'm not well studied on Euripides.) Pindar in Olympian 6 calls Pitana a parthenia (daughter of unmarried woman) and mentions her hiding in her mother's robe.

Based on examples like these, the scholar Giulia Sissa is of the opinion that parthenos is a social status rather than a biological term. I'm inclined to agree, and I certainly don't find the concept a foreign one.

There's another word for bastard, skotios shadowy or dark, which also shows up in the Iliad (book 6), and the accepted explanation is that a bastard is one "born in the shadows" or "born in the dark." This has further significance because of the wedding procession in which the bride would travel from her house to the groom's house in public by torchlight. Torches are typical identifiers of a wedding, used in both the Iliad (Achilles's shield) and in vase paintings. Thus, one born outside of marriage is one born outside the publicly sanctioned union and lacks the social benefits that would come with (such as first-born succession rights). I may be misremembering here, but I believe that Euripides also describes Ion as being born "without torches," which would of course connect these two terms for bastardy in a tangible way.

Hopefully this is a good starting place while you wait on other historians to answer.