Before we discuss the depictions of marriage in the Theogony, the Homeric Hymn to Demeter and the Odyssey, perhaps we should first discuss the real- life ancient Greek marriage rituals and reveal their attitude towards marriage.
Indeed, many of the things we see in Greek myths happened in real life as well. For example, the Greek girls usually married quite young, around the age of 14, which was meant to ensure that the girl was a virgin and pure in mind and body. "Marriage to a family member was an acceptable alternative and occasionally encouraged in order to consolidate family wealth"- if we look at many of the marriages between gods (taking only this example), we will notice that many of them were affiliated. Remember, for example, that almost all of the Olympian Gods were in some way related, most of them being brothers and sisters, and that many of them were married, like Zeus and Hera, for example.
If we are to refer to the Odyssey, one of the first things that comes to mind and should be mentioned is the concept of homophrosune, that is, "the union of the hearts and minds of a married couple." This ideal union could also happen between two friends or between a host and his guest, but in the Odyssey it is used to reflect this type of ideal communion between husband an wife. As we can read in the Odyssey, Odysseus explains at one point to Nausicaa:
And for thyself, may the gods grant thee all that thy heart desires; a husband and a home may they grant thee, and oneness of heart a goodly gift. For nothing is greater or better than this, when man and wife dwell in a home in one accord, a great grief to their foes  and a joy to their friends; but they know it best themselves."
Notice that in this reference, the term is used to depict the ideal relationship between husband and wife. However, at another point in the Odyssey, Telemachos tells Nestor's son: "Friends from of old we call ourselves by reason of our fathers' friendship, and we are moreover of the same age, and this journey shall yet more establish us in oneness of heart." Here the use of the term is somewhat nuanced and become the second alternative, that is the ideal relationship between two friends.
These two different situations in which the term is used make me consider the fact that Greek marriage in the Odyssey was seen as both a relationship of love, but also a relationship of friendship. Indeed, the two partners are friends and they live "in a home in one accord."
If we look upon Homer's works, we will notice that, besides the usual way in which a marriage is contracted, between the two parties, it is sometimes the case that a wife is won in a competition or is stolen by the husband. The War of Troy comes to mind here: Paris steals Helen away from her lawful husband so as to marry him himself. It is, however, my opinion that this is not seen as an act of bravery, but rather considered a treachery. In Homer's Iliad, Paris's act is an insult to the entire Greek civilization and a direct cause of the war to follow. So, while practiced, winning or stealing a wife seems to have a rather negative connotation.
If we think of the Odyssey, the whole fundamental concept of the poem seems to revolve around Odysseus's marriage with Penelope and his love for her. Indeed, this is the propelling force that carries him home and that makes him overcome all troubles. This is certainly an ideal marriage: in spite of the fact that Odysseus has been at war for 20 years and away from his home, Penelope has decided to wait for him and refuses to marry anybody else, even if the household is assaulted by numerous matchmakers who want Odysseus's wife and his throne.
Referring to the marriage concept here, the first thing that comes to mind is obviously the loyalty Penelope displays. However, there is another interesting aspect worth mentioning and discussing. Before Odysseus leaves for the Trojan War, Penelope has already given birth to a son. This is of utmost importance and shows the fact that in Ancient Greece, a first born son assumes all the importance that is later given to him in history. Indeed, Telemachus is the heir of the Ithaca Kingdom and the bond between Odysseus and his wife. We are able to speculate on the fact that, has this child not been born or had Penelope been sterile, Odysseus would have probably settled in one of the other kingdoms on the way and would have probably married a king's daughter, like Nausicaa, daughter of King Alcinous. We may consider that it is also because there is a son in the marriage that Odysseus does his best to return home.
Related to this, we can mention that in Greek culture, the woman followed a three stage evolution process, as is mentioned in one of the quoted articles. Initially, before her marriage, the young Greek woman is a parthenos, that is a maiden, only to become "a nymphe, a married woman without children, when she married" and "a gyne, an adult woman, when she bore her first child." If we check Penelope's evolution, she has already reached the last stage, which gives her infinite more rights and a more powerful position that if she had been only a nymph. She is, at this point, a true matriarch of the household.
A final thing we should mention when referring to the Odyssey and to the depiction of marriage here is that, according to some versions, after Odysseus's death, Penelope marries Telegonus, who is the son of Odysseus with Circe. If we are to briefly analyze this version, we will notice that this is in perfect concordance with many of the Greek myth, in which, after the husband's death, the wife remarries someone from the family. We have mentioned this before, related to the Greek society that partly encouraged marriages within the family.
If we think of the Theogony, marriage here seems to take a rather cosmic aspect, both through its manifestations and its implications. According to this, Chaos was the first element in the Universe, and after him came Gaea. She was "was the first being to arise from Chaos" and was "the mother of all things." She later crated Uranus, the sky, and Pontus, the sea. Her marriage with Uranus gives birth to the titans and the Cyclopes.
If we look at this aspect only, we can draw a conclusion on the role and depiction of marriage in the Theogony. First of all, marriage here means creation and offspring. It is obvious that this depiction is a positive one and we can associate it with everyday real life. In perspective, the most important goal of a marriage is to continue the family name and to provide offspring. If we look at Gaea's marriage to Uranus, this has a cosmological perspective, for having children here means creating life and providing the fundamentals on which civilization can later develop and the cradle from which all the other Gods are created.
If we follow the Theogony, we will see something that can be assimilated to family troubles. The father, Uranus, is somewhat of a tyrant and forces his children to live below ground. They rebel and mutilate their father with the help of Gaea, their mother. From the drops of blood that fall on the ground, a new generation of children is born, among them the giants and the nymphs. Her successive unions with Pontus and Tartarus give birth to a series of children, most of them monstrous beings that later challenge the Olympian Gods.
From the Theogony, we have several different depictions of marriage. First of all, here marriage is somewhat promiscuous and it seems that its only purpose is to bear children. Indeed, if we follow Gaea's evolution, we will notice that all her marriages have this main goal and that in many cases, marriage is not even mentioned, but the union of one to another.
Second of all, these unions, at least in Gaea's case, seem to create for most of the times, monstrous beings. I am not sure how this should be interpreted, but I may tend to see here a hidden critic from the writer, who doesn't necessarily see all these successive unions with good eyes. On the other hand, Gaea's cult will later be assimilated partially to the cult of Demeter and Gaea will always be regarded as the Mother of all things, the Creatrice of Life.
Third of all, marriage and union between brother and sister and between the members of the family is most common. Indeed, all the way to the Olympian Gods, everybody seems related in one big family. Zeus and Hera…