Some scholars hypothesize that both Frigg and Freyja may have their origin in a Common Germanic goddess. There is no firm evidence for this, but scholars have found some similarities both in their mythological features and the possible etymologies of their names, as well as place-names associated with them.
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The day of the week Friday in Old Norse is called both Freyjudagr and Frjádagr (for Freyja and Frigg respectively), in Faröese Fríggjadagur, and in Old High German was Frîatac, Frîgetac, and now Freitag, for Frigg. In Old English Frigedæg referred to Frigg as well.
The name of the early English goddess is attested only in the name of the weekday, although frīg (strong feminine) as a common noun meaning "love" (in the singular) or "affections, embraces" (in the plural) is attested in poetry.
Source: Frigg and Freyja origin hypothesis. (2016, October 1). In Wikipedia, The Free Encyclopedia. Retrieved 22:25, October 1, 2016, from https://en.wikipedia.org/w/index.php?title=Frigg_and_Freyja_origin_hypothesis&oldid=742135256
3 Answers
This is a convoluted topic, and I will start from a somewhat different angle: we are told by Snorri (and find confirmation in Völuspá) that Freya was for a while married to a figure by the name of Od, who subsequently disappeared and whom she cries tears of gold for.
The name "Od" is of course related to "Odin". This has led to the obvious identification of the two, even if it does not make much sense for Odin to get away with marrying two different goddesses without them realising.
This leads to the idea that not only Odin but also Frigg has been doubled; there are, as you have noted, considerable overlap between Frigg and Freya, but there is no firm proof, as they are also kept clearly separate in a number of stories. The etymology of their names is also different: "Freya" means ruler, while "Frigg", as noted, means "beloved".
Furthermore, in the admittedly late Sörla þáttr, Freya is referred to as Odin's "mistress", and it is told that they live together.
So, the answer to the original question is that there is strong support for the idea that Freya and Odin had some sort of relationship, even if it is difficult to answer properly of what kind. Perhaps the confusion it is a matter of different traditions getting mixed up, one where the pairing is between Odin and Freya, and another where it is Odin and Frigg.
The Eddic poem Hyndluljod, a dialogue between Freyja and a giantess, also mentions Od. The giantess Hyndla taunts Freyja for being over-sexed: You ran to Od,/ ever longing."
I've seen their relationship rationalized as Freyja being Odin's "concubine", and it should be noted that many European rulers, even after Christianity, had wives from several different ethinic groups within their territory. So Freyja could have been a co-wife, or concubine, and this would not have been unusual. (Given her status, co-wife seems more likely.)
I should also mention that Lee Hollander, among others, sees Od and Odin as two sparate beings, and thinks the whole story is a version of the Cupid and Psyche myth. Out of my three dictionaries of Norse mythology, Lindow sees them as related, Simek has no opinion, and Orchard sees them as possibly connected but with no real way to tell. (Both Simek and Orchard see Od as essentially "Freyja's husband", whatever his connection to Odin.)
John Lindow points out (perhaps jokingly) that the difference between Od and Odin lies in the fact that when Odin travels, no one seems to miss him.
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Lidow is certainly joking or misinformed; there is the story of how Frigg took Odin's brothers Vili and Vé as husbands when Odin was gone, and Saxo tells a story of how an illlusionist "Mithodin" briefly took his place.– andejonsCommented Nov 5, 2016 at 20:15
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The problem with your question boils down to the chaotic nature of oral tradition, each region has their own stories and myths, some of which survived and others didn't. Much of what we know about Norse mythology is from Snorri Sturluson and later Christians who translated Norse works.
There are vague, but strong evidence that Odin and Freya probably had a relationship. As seen in the two answers before mine.
Another problem with your is the nature of Norse Gods. In some cases, Freya and Frigga were the same, in others, they weren't. Freya/Frigga alone makes your question difficult to answer since there's not much evidence about Frigga/Freya being the same Goddess. As I said before, Norse mythology is a chaotic thing since they didn't write down their myths.
In the end, we'll truly never know if Odin and Freya had a relationship, but we can never say, "there's no way Odin and Freya would've had a relationship." Anyone who knows mythology, knows they are the craziest stories out there.
