When did worshipping of ancient Greek gods come to an end?

Looking from a different angle, the Greek (and Roman, and Egyptian, and Nordic, etc) gods were organised as families; dad, mom, son, daughter (with a few extras). The monotheistic religions evolved from these by just keeping daddy. Christians put mom and son back in again.

People never stopped worshipping the old gods. They just reconfigured them.

The official end of Greco-Olympian worship was in 380 AD/CE with the issuance of an Emperor's Edict. The very pro-Christian and rabidly anti-pagan Byzantine Emperor Theodosisus issued, "The Edict of Thessaloniki"-(in a Greek city approximately 100 miles Northeast of Mount Olympus). Unlike the earlier Constantinian based Edict of Milan which legalized Christian across the Italian peninsula and much of the Roman Empire, Theodosius' more draconian, Edict of Thessaloniki, essentially nationalized Christianity, making it the statewide religion of Italy, Greece, Asia Minor-(present-day Turkey), as well as throughout many parts of the greater Roman Empire.

The nationalization of Christianity by Theodosius was also the official ending of centuries-(even millennial) old pagan institutions, such as the Theater, the Hippodrome-(Chariot racing), the Olympics (and possibly Plato's Academy, though I am not entirely sure when the Academy was officially closed). Theodosius' discontinuation of these age old pagan institutions, also included the ending of Olympian worship at the pagan temples, which were either destroyed or converted into Churches-(such as The Parthenon and nearby Temple of Hephaestus in Athens).

The publicly led evisceration of pagan institutions by Theodosius, was the official end of the Olympian religion-(though, I suspect that many Greek and Romans individuals,as well as communities, may have practiced their Olympian worship services cryptically, probably until the collapse of the Roman Empire around 476 AD/CE. By around 500 AD/CE, Olympian paganism would have been "out of fashion", even cryptically speaking, due to the ubiquity of Christianity within Medieval Greco-Roman societies).

That's a bit of a tricky question. With many religions vestiges will remain centuries after the original was long abandoned. One well-cited example is the St. Bridget's relationship with Brigid. Does modern veneration of the Celtic Saint mean that the original religion is still alive? Also, to what extent does identification of a religion with Greece/Rome mean that a religion should be considered Greco-Roman? The Romans had a reputation of appropriating other deities into their pantheon. Does their incorporation of Isis make Isis a Greek?

There is little doubt that paganism had lost majority status in the cities before the time of Augustine. City Of God (426 AD) was written, at least in part, as a refutation of those who would have pagan beliefs return. There were a number of battles over the political clout of religion after Constantine, but from an official perspective, it was all but dead by 491.

That said, the very word "pagan" has its etymology in the word "rustic". While the cities certainly did not have non-Christian sects after the fifth century, the traditions and beliefs of those who lived in isolation continued much, much later. Depending on your interpretation of what "the old religion" is/was, you could effectively argue that it never died out but rather lives on as "witchcraft". Indeed, if you take the witches of the Latin and Balkan peninsulas as practicing a variant of Etruscan religion, and you view that same religion as partially centered on Uni (who is a parallel of Juno), then the Ancient Hellenistic gods never died out.

From the 350s onwards, the emporer Constantius II introduced the death penalty for practising pagan rituals. Of course, it didn't die out then until much later, but interest would have significantly dropped as Christianity became more and more popular, eventually becoming the official state religion.

There are of course people who still practise these ancient religions today - modern pagans, found throughout the world, not just Greece.

If you read "Modern Greek Folklore and Ancient Greek Religion", by John Cuthbert Lawson, you will see that, as late as 1910, there were are least significant vestiges of original Greek religion. Other useful material can by found in the works of Jane Ellen Harrison.

I hesitate to try to summarize >300 pages here. Much of it is what you might call 'folkloric'. E.g., people who say that particular trees are Nyads. An important subset are nominally Christian practices that, linguistically or operationally, look just like ancient Greek goings-on. So, no, he does not cite any current (1910) examples of people sacrificing bullocks to Zeus. But he does cite animal sacrifices at the dedication of buildings.

So, it will all boil down to your definition of the word 'end'.