The mouth is the source of all language,
a pillar of wisdom and a comfort to wise men,
a blessing and a joy to every knight.
The Anglo-Saxon rune Os (according to a Wikipedia article which steadfastly refuses to cite its sources!) is one of three Anglo-Saxon runes that split from the Ansuz rune of the Elder Futhark. Because of the development of vowels in England at the time, the 'a' rune was split into an 'o' sound, an 'æ' sound and an 'a' sound. If I'm remembering my diction class correctly (which is debatable), the 'o' sounds like the o in 'moat', 'æ' sounds like 'cat' and, and 'a' sounds like the a in 'caller'. Os is our 'o' rune.
There is also a bit of controversy over the translation of the name of this rune. I discovered, by googling some of the information in the before-mentioned Wikipedia article with no sources, a lovely volume titled The Anglo-Saxon Minor Poems, Volume 6 by Elliot Van Kirk Dobbie. One of the poems he analyzes is the Anglo-Saxon rune poem, and his commentary has a great deal of information on the runes, as well as what seems like a wealth of sources - which I am, unfortunately, unable to see with the brief Google Books preview; I'll be ordering it through inter-library loan and will hopefully be able to update with more direct sources soon.
"The name os, given for this rune by Hickes, is perhaps the Anglo-Saxon word os, "(heathen) god"." He goes on to say: "In the Iclandic rune poem the rune (in a somewhat different form) stands for óss (or áss), "god," but in the Norwegian rune poem it stands for óss, "river-mouth, estuary." An alternative translation of the Anglo-Saxon rune name, by Kemble, Archaeologia XXVIII, 340, favored by Dickens and accepted by Keller, Anglia LX, 142, takes os as the Latin noun, "mouth." This meaning fits better with the [stanza of the Anglo-Saxon rune poem], "source of every language," but no other foreign words are found in the poem as the names of runes."
Given this evidence, I think it is reasonable to discount the Latin translation 'mouth' as a Heathen interpretation of the runes. I believe that Van Kirk Dobbie is quite correct in his supposition that the name for this rune translates to 'god', especially since the Icelandic rune poem, as noted in the quote, quite specifically mentions it (God // aged Gautr // and prince of Ásgarðr // and lord of Valhalla). Given the connections we know Woden has to the runes, language, and poetry; I don't think it's outside the realm of possibility that the line "the source of all language" may be referring to Him. Again considering the Icelandic rune poem, who would be the "lord of Valhalla" but Odin?
Now that we've analyzed the possible translations of Os, it's time to discuss the meaning of this rune and its possible implications in divination. My take on this is obviously going to be informed by my association of the Anglo-Saxon rune poem's stanza with Woden, so bear with my potentially over-reaching conclusions! I see this as Woden's rune, much like Tyr is associated with Tiw. We don't know much about how the Anglo-Saxons viewed Woden, and how those views may have been similar or different to the view of the Norse; and this rune poem was written a few generations off from un-Christianized Heathens. Nevertheless, I feel this rune's strongest associations are with Woden as a god of language and poetry; a poet's rune. To me, it would represent creativity, and the struggle that must so often be engaged in to let the creation come to light.