1) The Son as Image of the Father and the Spirit as Image of the Son.
2) Divine foreknowledge and predestination as an image of the future
3) Man, as in the image of God
4) Scripture, which images the invisible by analogies
5) Types or prefigurations
6) Memorials of the past that serve to glorify virtue and put vice to shame.
(The relevant passages can be found here and in Part III, here. The full text is here.)
Halliwell then goes on to say (pp. 336-337), "This scheme rather strangely interweaves species of 'image' (persons, mental ideas, visual representations, writing, physical objects) with the functions of images (as prefigurings, analogies, reminders, etc.). The results may strike us as awkward and lopsided, but the typology is clearly meant to reinforce the two general tenets of John mentioend earlier--that images are not tied to relationships of strict equivalence, and that they have the power to reveal that which is, in some sense, 'hidden'--and thereby to promote a series of options in the interpretation of religious images."
This is about right, although I'm unclear as to what sort of person would find it "awkward" or "lopsided" or "strange"; John, in writing about Christian icons, gives us a list of the primary types of icons or images that play a role in Christian faith, and there seems nothing strange about that. Indeed, there seems to me to be an elegance and balance to the list. Halliwell seems exactly right that the primary motivation of the list involves the issue of revelation. Just judging from the list here, it looks like we have a sort of hierarchy, going from the most perfectly and spiritually revelatory images (the Persons of the Trinity themselves) to the more materially limited revelatory images (reminders of the past); or from the more fundamental and basic revelatory icons to the least fundamental and derivative icons; or something along these lines.
Although Damascene just runs through them, from what I can tell he means by 'Scripture' not the written text as such - which is an example of (6) - but, as it were, the meaning of it, the images that are brought to mind, like light, or vines, or lions, which symbolize divine things. As he says,
For the invisible things of God since the creation of the world are made visible through images. We see images in creation which remind us faintly of God, as when, for instance, we speak of the holy and adorable Trinity, imaged by the sun, or light, or burning rays, or by a running fountain, or a full river, or by the mind, speech, or the spirit within us, or by a rose tree, or a sprouting flower, or a sweet fragrance.
Thus man is perhaps listed here as higher in the hierarchy (assuming I'm right about the hierarchy) in the sense that he is in some sense a direct image of God, while Scripture is more indirect, in that it presents to the mind images of God. It's perhaps also relevant that Christ became man. In terms of Christian experience, I suspect this is about right, and Damascene uses this internal structure of the iconic experience in the Christian faith (the mediation of revelation by icons/images of various sorts) to show just how important the very notion of an image or icon is to the faith. This is confirmed by the fact that he says in Part III, "either reject all images, and be in opposition to Him who ordered these things, or receive each and all with becoming greeting and manner."