Heliod, God of the Sun - Heliod is the god of law, justice, retribution and bonds of kinship.

Greek counterparts:

• Helios, Greek God of the Sun: the back stories of the two have a major similarity - Helios convinced Zeus to use his lightning bolt to wipe out Odysseus' men and ship after Odysseus' men kill one of the sacred red cattle on an isle sacred to Helios. Heliod, according to Theros legend, used his spear to smite a major polis and cast it into the sea. Helios was said to be crowned with a shining aura of the sun - Heliod has essentially the same thing, a presence so bright mortals cannot see Nyx when Heliod is present.
• Zeus, Greek God of the Sky and Thunder: Zeus is also the god of law; both Zeus and Heliod hold an elevated place in their cultures legal system. Heliod is invoked directly in legal proceedings and to ask for justice; Zeus was thought to ensure oaths were upheld and traders remained honest.
• Nemesis, Greek Goddess of Revenge, Balance, Righteous Indignation, and Retribution: Nemesis is known for luring Narcissus to a pool where he fell in love with his own reflection. Unable to leave the pool he eventually died. Nemesis did this because she disdained those with boundless gifts and took retribution on Narcissus for his great beauty. Given what we know of Heliod, retribution is central to his persona.

Magic Specific - Heliod's personality is friendly and gregarious while he makes allies easily. He does turn on them but unlike Greek Gods there is little to suggest active plotting against others. Being allies with mortals easily is also different than the Greek gods.

Thassa, God of the Sea - Thassa is god of ancient knowledge, murmurs, gradual change, introspection, vast distances, long voyages, and far-ranging searches.

Greek counterparts:

• Poseidon, Greek God of the Sea: The most obvious connections are the choice of weapon - Poseidon a trident and Thassa a bident - and the domain of sea and sea creatures. The stories of their wrath are not directly similar but either could theoretically have completed either - Poseidon sent a sea monster to attack Troy after the King of Troy betrayed his word to him; Thassa turned a sailor's family into eels after he stole her bident to destroy an enemy fleet.
• Athena, Greek God of Wisdom: Athena has many more attributes than wisdom but that is the primary one of concern with regards to Thassa. Athena is also associated with helping heroes on their quests which ties into "vast distances, long voyages, and far-ranging searches".
• Thalassa, a Greek primordial sea goddess: Thassa's name is likely derivative of Thalassa.

Magic Specific - Blue's portion of the color pie leads to the always wanting change but slowest to action of Thassa which is generally not what Greek gods wanted - they often enjoyed change for the sake of change but they were impulsive and not restrained.

Erebos, God of the Dead - Erebos is the god of misfortune, ill fate, begrudging acceptance, envy, bitterness, and wealth.

Greek counterparts:

• Hades, Greek God of the underworld, the dead, and the earth's hidden wealth: Hades is obviously the primary inspiration for Erebos and perhaps the most obvious of the relations of Theros and Greek mythology. Contrary to popular modern conception Hades was not evil; mainly he has passive though cruel to those who tried to betray him either by cheating death or trying to leave his realm. This is very similar to Erebos, though Erebos is less interesting in those trying to cheat death as he knows all mortals will eventually join him. Both Erebos and Hades are strongly associated with wealth due to the accumulation that the dead bring with them as well as being the "under world" where gold is common.
• Erebus, a Greek primordial deity, representing the personification of darkness: Erebos is pretty clearly a derivative of Erebus - in some cases in Greek Erebos was used. Erebus is also said to have been one of the first beings, born of Chaos, and with him came darkness. Erebos was born of Heliod's shadow when it was first cast which has some connections to Erebus' origin.

Magic Specific - The largest difference is in that Erebos seems very restricted to his realm, he is said to envy the sunlit world, implying little ability to experience it.  The Greek Gods had much more freedom of movement as they pleased (though Hades spent most time in the underworld it was his choice)

Purphoros, God of the Forge - Purphoros is the god of the restless earth, fire, artisans, obsession, and the cycle of creation and destruction.

Greek Counterparts:

• Hephaestus, Greek god of blacksmiths, craftsmen, artisans, sculptors, metals, metallurgy, fire and volcanoes: Hephaestus is the smith of the gods armor and weapons and generally any relic of significance. He is considered the male counterpart to Athena in that he inspires mortals and teaches them the arts. Purphoros inspires just simply by being around others. Purphoros also pushes the boundaries in his crafts; Hephaestus craft grew as well, enough so that he was taken back into Olympus after having been exiled.
• Poseidon, Greek God of Earthquakes: This is a lot of interpretation on my part, but if "restless earth" includes earthquakes that was Poseidon's realm.
• Periphetes, son of Hephaestus and Anticleia: The inspiration for the name Purphoros was difficult for me to find, and this seems the closest but it could be something else entirely (or just a name without a direct inspiration conscious or not)

Magic Specific - Purphoros seem to be willing to share his works and techniques much more readily with mortals than his Greek counterparts.

Nylea, God of the Hunt - Nylea is the god of the hunt, the seasons, the forest, and of metamorphosis and rebirth.

Greek Counterparts:

• Artemis, Greek god of the hunt, wilderness, animals, young girls, childbirth and plague: In Roman mythology Diana is the counterpart to Artemis and WotC said in a recent Arcana that Diana is the inspiration for Nylea. Artemis and Nylea have a lot in common - both are the best hunters and defend that title. Both anger easily and will punish those that hunt in their realm without their permission.
• The Greek goddesses of the seasons, Eiar, Theros, Pthinoporon, Cheimon (spring, summer, autumn and winter): Nylea is in control of the seasons and decides when each occurs. This also shows where the whole block name comes from...

Magic Specific - Nylea's major difference is her abhorrence of temples of worship and sacrifices made in her honor. Greek gods had lots of temples and often demanded sacrifices. I was unable to find something that seemed plausible as an inspiration for the name Nylea. If you know of something please include it in the comments!

Spear of Heliod - The full name is Khrusor, the Sun Spear. Heliod can pitch down Khrusor from the heavens to any point on Theros.

Possible inspiration:

• Zeus' Thunderbolt - The main correlation is the ability to be thrown from the heavens as needed. There are also the similarities of Zeus and Heliod to consider.

Magic Mechanical Flavor - The intention seems to be awe inspiring as well a weapon of retribution, both aspects of Heliod.

Bident of Thassa - The full name is Dekella. It is a two pronged spear. Wielding Dekella allows control of the tides and the ability to stir up whirl pools.

Possible Inspirations:

• Poseidon's Trident - Poseidon is said to have been able to create waves, whirlpools and tsunamis with his trident, the same as Thassa. Being the weapon of the god of the sea is usually correlated to the tridents use in fishing.
• Hades' Bident - This is perhaps the most famous bident and listed here for completeness. 

Magic Mechanical Flavor - In magic lore drawing a card is akin to gaining knowledge. Thassa is the god of ancient knowledge and secrets of the briny depths so the card draw is appropriate (it is also a throw back to Coastal Piracy due to the sea them of the same mechanic). Forcing creatures to attack could be seen as manipulating the seas to direct voyages where Thassa deems fit.

Whip of Erebos - The full name is Mastix. It is golden handled and  has an "impossibly long lash".

Possible Inspirations:

• I was unable to find anything that seemed feasible as an inspiration. There was no major mention of a whip for the Greek gods and very little overall in mythology. Erebos' whip only real correlation is Cerberus simply because they both worked to keep the dead in the underworld, but that is a tenuous connection.

Hammer of Purphoros - The full name is Akmon. Striking metal with it causes sparks of enchantment that come to life.

Possible Inspirations:

• Hephaestus' Hammer - The hammer of Hephaestus doesn't have a particularly special place in Greek mythology. It served as one of his symbols and was used in crafting the various weapons and armor of the gods.

Magic Mechanical Flavor - The first ability has little connection to what we know of Akmon, just that is it very red. The second ability fits very well as Akmon can strike the earth (lands) molten and create something from that.

Bow of Nylea - The full name is Ephixis. There is no lore or details on the bow other than it being a short bow.

Possible Inspiration:

• Artemis' Bow - When Artemis' was a child she asked Zeus for 6 wishes, one of which was a bow and arrow. It is thought Artemis' Bow was gold or silver and among the most famous of the time.

Magic Mechanical Flavor - The first ability is fitting as Nylea would likely want clean kills as she is okay with predation but despises hunting for sport. The second ability seems very awkward and forced. From articles on the mothership we know it's supposed to represent the 4 seasons, a key part of Nylea. The implementation however is just a complete miss - which choice is winter? Summer? Why that one?

Minotaur - A major difference with minotaurs of Magic and Greek myth is the number - in Greek myth there was only 1 Minotaur, in magic there are many - and that is the case with many of the monsters. In the Greek myth the Minotaur is born from Pasiphaë and a bull. The gods made Pasiphaë fall in love with a bull in retribution for a grievance against Poseidon by her husband. The Minotaur was born and grew quickly, eventually needing more nourishment than nursing could provide, thus he started devouring man. He was always ferocious and bestial; eventually he was put into the labyrinth. In Theros the minotaurs are wild and very bestial. Their favorite meat is human.

Sea Creatures - The primary source in Greek myth of sea creatures comes from Odysseus in Odyssey. During the return trip to Ithaca Odysseus had to pass between a sea monster and a whirlpool - Scylla and Charybdis respectively. The "whirlpool" is sometimes a whirlpool and sometimes a giant monster who sucks in water with enough force and volume to create the whirlpool. Both were said to be born of the gods or had special attention paid to them by the gods. On his journey Odysseus ran into many sea creatures from Poseidon. In Theros the creatures are just large creatures that cause havoc. The most dangerous portion of the Theros creatures is their ability to breathe air for some period of time potentially causing destruction on land as well.