The answer depends on what is signified by oldest. If you take oldest to mean oldest in their existence in the world, then <PERSON> and others beings of his ilk qualify to be called the oldest in Arda. These were the oldest beings in Arda
* Ungoliant
* <PERSON>
* Possibly the Watcher in the Water
* Many other unnamed entities lurking in the deep places of Arda.
In fact <PERSON> states unambiguously from his point of view that he was there in Arda before the Dark Lord (Morgoth).
"Eldest, that's what I am... <PERSON> remembers the first raindrop and the first acorn... He knew the dark under the stars when it was fearless - before the Dark Lord came from Outside."—
<PERSON> (Fellowship of the Ring)
How could a creature or being in Middle Earth be older than one of the Ainur who we know are spirits created by <PERSON> before the creation of the World? This would be possible only if <PERSON> and other beings like him were created with Ea and were inseparable parts of the World in the thought of <PERSON>. Thus to him, <PERSON> and the other Ainur would be outsiders who appeared later on Arda.
In <PERSON>’s universe, the Ainur are those spirits which were with <PERSON>, the Creator before the creation and participated in the Song of Creation. They were meant to be active participants in the making and shaping of the world. But not all spirits in Arda could belong to the category of Ainur. Arda is populated by various other spirits which were not Ainur but came into being with the creation of the World. 88
These beings didn't participate in the Song of the Ainur because they didn't exist before the creation of the world. They were beings created with the World as an embodiment of certain archetypes.
Though the Ainur being products of <PERSON> thought had existed outside of the created world as expressions of various aspects of His Mind, it is only after the creation of Ea that they (Ainur) enter Time and Creation.Thus they would innately be less "older" compared to the beings which were created with the World and had always been a part of it.
<PERSON> who allies with <PERSON> to destroy the two trees is one of these other spirits.
Some have said that in ages long before she (<PERSON>) descended from the darkness that lies about Arda […] in the beginning she was one of those that he corrupted to his service. But she had disowned her Master
– The Silmarillion, ‘Of the Darkening of Valinor’; Chapter 8
She is the archetype of primordial darkness and the Void and her trying to devour <PERSON> foreshadowing of <PERSON>’s ultimate fate of being cast out into the Void.
The Watcher in the Water, the creature the Fellowship encounters at the gates of Moria was another of primordial "other" spirits.The name “Watcher in the Water” itself seems to suggest that this being’s existence was inextricably bound to the waters and that it was a guardian for the lakes beneath the mountain.
“I felt that something horrible was near from the moment that my foot first touched the water,' said <PERSON>. 'What was that thing, or were there many of them?'
'I do not know,' answered <PERSON>; 'but the arms were all guided by one purpose. Something has crept, or has been driven out of dark waters under the mountains. There are older and fouler things than Orcs in the deep places of the world.' He did not speak aloud his thought that whatever it was that dwelt in the lake, it had seized upon <PERSON> first among all the Company.”
-The Fellowship of the Ring, Chapter 4 "A Journey in the Dark"
The existence of beings other than the Ainur in the "deep places of the World" is also hinted at by <PERSON> in his words to his companions.
And this
Far, far below the deepest delvings of the Dwarves, the world is gnawed by nameless things. Even <PERSON> knows them not. They are older than he. Now I have walked there, but I will bring no report to darken the light of day.
-The Two Towers Book III , Chapter 5: "The White Rider"
Thus we can conclude from examples scattered throughout the text that there were indeed beings older than the Ainur in Arda that were “nature spirits” whose very existence was tied up with the World. 381