The eldil are sort of a kind of hnau (Hyoi himself does not know) and are like messengers that give messages to the hnau and speak to them. They are very hard to see, and for the most part, can only be seen when chosen to be seen.
The greatest eldila on Malacandra is Oyarsa.
On Malacandra, their word is considered law. For example, during the hunt for the hnakra, Hyoi, Whin, and Ransom were visited by an eldil who told them that Ransom needed to go to Oyarsa straight away. Because they disobeyed this (they went to go kill the hnakra instead), Hyoi was shot by Weston and therefore died.
In the Malacandran tier of hierchy, they come between the hnau and Maleldil.