When I went to think of what would work for O, the first thought that came to my mind was oikos, and that itself is perhaps the most important part of the Hellenic religion. The oikos, or home, is the center of worship which is complimented by the numerous components of the public religion. The oikos even has its own set of gods as it were, or rather specific epithets of particular gods as they relate to the functions of the home.
Hekate, who really isn’t a very major public goddess, is an important one in the oikos. She, and/or arguably Artemis, stands at the entrance of the home itself as goddess of the portal (something which is attributed to both goddesses, and as I have seen imagery of both goddesses for the entrance of the house I just accept both at that place in my own household). As such we see a goddess who is associated with the welfare of the house, likely by keeping harm from entering the oikos as well as ensuring good welfare,prosperity, and new life. Such works for either Hekate or Artemis, and as a feature of the oikos itself, the placement at the front door entrance is important.
Of course there is another pair of gods who does something quite similar, and they are at the gates of the oikos. Now for those of us who have no clue because our houses lack such features, houses had (and in Hellas there are many houses that continue to have) a kind of courtyard. So there is a difference from entering the gated property, and entering into the home where the hearth was. At the gate the protection and prosperity is overseen by Hermes and Apollon Agyieus, the latter who is represented by nothing more than a large conical stone wreathed, onto which offerings to the god were poured. These are the gods to whom one would pray as they are leaving and entering the property daily…mostly likely, in ancient Hellas, by men, as in most cases women (who were likely the most responsible for the offerings to Hekate/Artemis) ventured out less often. In a modern home it is natural to just combine the two if you have an apartment. For a house with a yard, the property boundary at the end of the drive would probably work, but for those us who lack this, honoring Apollon Agyieus and Hermes at the door with Hekate/Artemis works just as well. It serves much of the same function, just more like a double barrier as far as I see it for gods that are so intimately associated with the liminal places.
Within the household then you have two aspects of Zeus and Hestia. You have Zeus who dwells at the center of the house, who, it seems reasonable to me, was probably honored at the hearth with Hestia, as the hearth was the center of the home. I use this logic to honor him together with her. Of course again we have challenges for our modern living because we no longer, in many cases, have a hearth at the center of our home. Some go literal and look for a continous fire source, and therefore choose the pilot light on their stoves and set up for Hestia in their kitchen. I go less literal and more symbolic. Sheis the goddess of the hearth, she who dwells at the center of the household. The center of the household is typically the living room where the family gathers, and where the hearth would be if there was one. So it is appropriate to offer to Hestia and Zeus at the center of the house. The second Zeus is Kthesios, a serpentine Zeus of the pantries who protects and perserves your provisions and brings prosperity, and who is honored by the making of a jar filled with grain and fruits of the earth, as a regular offering to him.
These then more or less make up the regular gods of the oikos. Then we continue on to those gods which are honored within the oikos at certain times of the month. Selene would be one I would wager, and Apollon Noumenios at the beginning of thenew month with the visible moon cresent. The second day is followd with honoring the Agathos Daimon, the good spirit, though there seems to be perhaps two..one general agathos daimon of the household, and a personal agathos daimon. Athena is honored on the third day of the lunar month, and Hermes on the fourth (though he is also honored on that day with Athena, Herakles, Poseidon, Aphrodite, Eros and Apollon). The fifth is for the Erinyes/Eumenides and Orkos. This is an interesting set particularly because the Erinyes (Furies) are associated with the protection of blood-relation, punishment of violations against it, but are also goddesses who bring prosperity as we know from Aeschylus’ Eumenides. The sixth of the month is the day of Artemis, while the seventh is for Apollon as well as being holy for Hermaphroditos (I do have some ideas of why Apollon would share a holy day with Hermaphroditos, and this has something to do with a comparison between the male-female identity of Hermarphroditos, and the male-female unity of the twins Apollon and Artemis conceived from the same womb). The tenth is a general holy day, and the 12th is for the Moirae (Fates). As the domestic calendar is divided into three parts (being three parts of the month) we end up seeing alot of repetition throughout the rest of the month with days for the Erinyes, Artemis, Apollon, Athena etc.
The thing to keep in mind is the oikos is the heart of Hellenismos. It is where children are born, named and reared, where culture is passed on, and where the myths are retold and the gods worshiped first and foremost. It is religion admist the very center of our lives, and part of our most intimate routines. While the festivals are grand, nothing compares to the religion of the oikos as our daily religious lives and interaction with the gods. It is an essential part of our religious/spiritual lives.