This is a tough question to answer. I can only speak for the Seleukids, Parthians, and to a degree the Ptolemies.

First, I will start with previous notions of how the Hellenistic world was conceived. The idea was for a somewhat colonialist idea whereby Hellenes (Greeks and Makedones) ruled over and attempted to "civilize" the non-Hellenes from the Persians, to Baktrians, to native Egyptians. This is a dangerous proposition, and as elucidated by numerous historians, utterly unacceptable when describing the Seleukids and other Hellenistic dynasties.

For the Seleukids, there is nothing to suggest that there was a strict hierarchy that differentiated between the Makedonian Seleukids and the Iranian natives in Media, Persis etc. In many cases, there are examples of Iranians rising to high ranks, like the case of Bagadates who was appointed as a frataraka of Persis, which is an important position. Further, according to Polybios, Livy, and Diodoros, there are many indications that the Seleukids employed Iranian contingents in their armies ranging from Persian archers to Median cavalry

All of this is to showcase that there were high positions for these natives in the Seleukid apparatus. Then we go to the idea of military colonies as these were primarily settled by Hellenes. However, a lot of work done by Bar-Kochva has shown that often non-Hellenes were in these colonies, such as Jews in Asia Minor as well as Medians in Iran. In that sense, we can see a degree of a somewhat egalitarian viewpoint created by the Seleukids in which the very diverse subject populations were allowed to more-or-less do as they wishes. But in doing this, we must note "exceptions." The prime example is the Maccabean revolt; traditional narratives from the book of Maccabees suggests that the reason was that the Seleukids were imposing traditional Greek religion on the Jews who were affronted and thus revolted. This idea has been severely challenged, and the current consensus among scholars is that the Seleukids merely got involved in a Jewish civil war. This arises because traditional Seleukid practice had been to support Hellenism where they could by paying for gyms, bouletarians, etc (the process is known as euregetism). But it was never to be imposed upon, just supported if the population accepted it. In the case of Judea, some Jews had become Hellenized where some were conservative in their culture; thus some of these Hellenized Jews asked for the king Antiochos IV to help with benefaction, and the king had no problem with it. However, the conservative faction was not pleased and this lead to the conflict of which led to the revolt.

Now we get to the idea of a unifying nature of Hellenism. This is tough to answer, but on the whole it seems that there was a connected Hellenic world during this period. An example is that in Baktria in the city of Ai-Khanoum, the general plan of the city is very similar to poleis in Asia minor. Even with this far of distance, there was the notion of a connected world. And really, that is the major point that is missed: when one sees political borders, one may immediately think of divisions and places where he cannot go. This was not the case at all, and in many ways there was extensive movement in this world by all sorts of people, including Hellenes. And with that, they brought their culture and way-of-life to their new homes. But while it maybe somewhat realistic to consider a sense of Hellenic elitism over a non-Greek population, in many cases there was cooperation and understanding (the kings of Baktria employed Persian cavalry contingents, without whom their conquest of northern India would have failed). The point is to emphasize cooperation rather than hostility when examining this stage of history, and luckily the Hellenistic world is truly an age of cooperation.

Ok, with that being said, we can move onto the Parthians. Historians have traditionally seen them as a sort of Persian empire reborn. However, the Parthians (who I will call Arsakids because of the dynasty) were NOT Persian, but an Iranian monarchy that led the Skythian Aparni tribe. And in this, they were very much a Hellenistic monarchy as they would adopt many Hellenic cultural elements in their ideology (see excavations in Nisa). Hellenes too would be held to a relatively high position in the empire. We know that Hellenes in Seleukia-on-the-Tigris were taken good care of by king Mithridates II. Further, a letter from the king Artabanos II to the bouletarian of Susa is revealing--here is the link: http://parthia.com/artabanus2_letter.htm

It shows that the city of Susa retained a polis form of government and that Hellenes would often be leaders of this government. The system is not too divergent from how polis interaction and governments worked in mainland Hellas and Asia Minor. Once again, the theme is cooperation and connections; despite being in the "Persian" part of the world, these Hellenes still acted and governed themselves like they were in Greece. Their relationship with Iranians is unclear, but being that a man names "Phraates" could be archon means that the two cooperated out of necessity. This is certainly true for the Arsakids who would adopt Phi-Hellenic images into their state ideology and employ Hellenic soldiers and generals in their wars.

Going to the Ptolemaic dynasty, things are much more different. For one, there was a clear social stratification with Hellenes on the highest echelon, the Egyptian priestly class, and then native Egyptians. However, we would be foolish to think of this system as wholly elitist, as there are some papyri that showcase well off Egyptians. In particular, the priestly class was favored as the dynasty co-opted religious systems to recreate the idea of a divine monarchy. All of these things are Egyptian in origin, and rather that Hellenize the population, there was a move to appeal to them ideologically. This can be seen in the Canopos decree or even the famous Rosetta decree as they had three languages: Greek, Egyptian hieroglyphics, and demotic corresponding to the different groups in the empire. The king was playing for all of them rather than just Greek and expecting everyone to learn it.

That being said, there are cases of exploitation, as there is a famous papyrus where a native Egyptian was appealing to help from the king after being swindled by a Greek merchant. The man claims that he cannot get proper recourse because he cannot "Hellenize." In the end, the system was meant to benefit the king and his Hellenic subjects, so this event is not unusual. As a general idea on these Greeks, they were from many places, and many would settle in Alexandria where some would complain about the native Egyptians (source is a play from Alexandria, but I cannot remember from where).

I hope this answers your question, and if you have anymore, please let me know!

Sources:

Primary-- Diodoros, World History

Herodotos, Histories

Livy, Roman History

Polybios, Histories

Secondary: Assorted articles from the Encylopedia Iranica

From Samarkhand to Sardes, by Susan Sherwin-White and Amelie Khurt

Greek World after Alexander, by Graham Shipley

Hellenistic World from Alexander to Roman Conquest, by Michael Austin

parthia.com