Welcome back to Runes 101. Who, in Norse Mythology, knows the Runes? We know that, for the Aesir at least, Odin grabbed the Runes and learned them. The poem "The Sayings of Har", also called "The Sayings of the High One", tells us this. What happens once Odin has the Runes and gains insight and knowledge from them? Does he share this information with the chiefs of the other kingdoms in the world of Norse Mythology or do they acquire the knowledge in some other way? The former seems unlikely to me; Odin does not strike me as wanting to share knowledge with other chiefs. After all, he was willing to sacrifice his eye so that he alone would have the knowledge held within Mimir's Well of Wisdom. The latter option - the other chiefs learning the magic of the Runes in another way - remains a mystery. We don't know how they came to understand the Runes; we know only who they are.
In verse 143 of the same poem, it says that Odin among the Aesir, Dain for the elves, Dvalin for the dwarfs, and Alvith/Asvid for the giants. These lines suggest that these are the "Rune Readers" for each of these kingdoms. The last line of this verse says basically, "I carved some for myself." Based on the other references to "I" in the poem, it appears as though this is Odin saying he carved his own Runes. There is no mention of how the other three gain their knowledge of the Runes. Interestingly, no Vanir (the other kingdom of gods) is mentioned as having this ability.
The Vanir are defined, typically, as fertility gods, gods/goddesses who have the ability of seidr (a form of witchcraft and trances). They can see the future. Can they, too, read the Runes? This is a question I cannot answer, but I can offer some food for thought. Some scholars and researchers suggest that Heimdall may have been part of the Vanir kingdom. We know that Heimdall knows the Runes, because the Rigsthula myth tells us how he comes out of the forest and greets Jarl, his son. Rig, who is Heimdall, teaches Jarl the Runes. So, could Heimdall be the Vanirs' Rune Reader? One last bit of fodder for those of you who don't know Rigsthula - Jarl is a human, a king. Who gets credit for giving the knowledge of the Runes to humans then? Heimdall or Odin?