Godhead= Divinity or Deity
The noun G2305 θειότης theiotes meaning divinity, and the adjective G2304 θεῖος theios are not remarkable, gem, enigma nor do they reveal a mystery. "Divinity" is a noun that refers to the quality of being divine or having divine nature. The words used for Godhead mean deity or divinity, state of being divine; godhead, godhood or god-ness. See Godhead on ISBE, and on A Dictionary of the Bible- Dealing with Its Language, Literature, and Contents, Including the Biblical Theology, By John Alexander Selbie, 1899.
The three references (compare English and Latin), you have cited are derived from the same root word theos, synonyms and inflections. Inflection is the change of form a noun, adjective, verb, etc., undergoes to distinguish its case, gender, mood, number, voice, etc.
The Acts 17:29 ref Θεῖον (see theios) is an adjective, accusative; in Romans 1:20, it is a noun in nominative; and in Col 2:9, a similar word in genitive. One is adjective, two are synonymous abstract nouns. The two nouns are to be analysed.
Theotes and Theiotes
Theotes and Theiotes are abstract nouns. Theiotes is a noun derived by adding the tes suffix to the adjective theios; whereas the former, Theotes is an abstract noun derived by adding tes to the concrete noun Theos which is the root word for all 3 words. Abstract nouns are those which are intangible, describing a concept, as opposed to concrete or common nouns which refers to a particular object or person which is tangible and real. There is an excellent answer here with the lexical analysis Theotes, on the Colossians verse question.
Theotes and Theiotes are therefore synonyms, as listed in Thayer's lexicon:
θεότης, θεότητος, ἡ (deitas, Tertullian, Augustine (de 104: Dei 7, 1)), deity i.e. the state of being God, Godhead: Col 2:9. (Lucian, Icar. 9; Plutarch, de defect. orac. 10, p. 415 c.)
(Synonyms: θεότης, θειότης: θεότης deity differs from θειότης divinity, as essence differs from quality or attribute; cf. Trench, sec. ii.; Lightfoot or Meyer on Colossians, the passage cited; Fritzsche on Rom 1:20.)
To simplify, θεότης is the concrete noun based abstract noun; and θειότης theiotes with an i is the adjective based abstract noun; as the following describes, theiotes expresses a more general divine attributes as understood from Romans and Acts context; whereas theotes expresses a more essential divinity, it is focused towards a more definite sense, a concrete or proper God, as in Colossians. I searched the two words with "church fathers" on google books advanced search, and to quote from Synonyms of the New Testament, Fifth edition, revised By Richard Chenevix TRENCH (Archbishop of Dublin.) · 1871; which is actually available in digital format:
θεότης and θειότης: And that this distinction between ‘deity’ and ‘divinity,’ if I may use these words to represent severally θεότης and θειότης, is one which would be strongly felt, and which therefore would seek its utterance in Christian theology, of this we have signal proof in the fact that the Latin Christian writers were not satisfied with ‘divinitas,’ which they found ready to their hand in the writings of Cicero and others; and which they sometimes were content to use (see Piper, Theol. Stud. u. Krit. 1875, p. 79 sqq.); but themselves coined ‘deitas’ as the only adequate Latin representative of the Greek θεότης. We have Augustine’s express testimony to the fact (De Civ. Dei, vii. 1). ‘Hanc divinitatem, vel ut sic dixerim deitatem; nam et hoc verbo uti jam nostros non piget, ut de Graeco expressius transferant id quod illi θεότητα appellant, &c.;’ cf. x. 1, 2. But not to urge this, nor yet the different etymologies of the words, that one is τὸ εἰναί τινα θεόν, the other τὸ εἰναί τινα [or τι] θεῖον, which so clearly point to this difference in their meanings, examples, so far as they can be adduced, go to support the same. Both θεότης and θειότης, as in general the abstract words in every language, are of late introduction; and one of them, θεότης, is extremely rare. Indeed, only two examples of it from classical Greek have hitherto been brought, forward, one from Lucian (Icarom. 9); the other from Plutarch (De Def. Orac. 10): οὕτως ἐκ μὲν ἀνθρώπων εἰς ἥρωας, ἐκ δὲ ἡρώων εἰς δαίμονας, αἱ βελτίονες ψυχαὶ τὴν μεταβολὴν λαμβάνουσιν. ἐκ δὲ δαιμόνων ὀλίγαι μὲν ἔτι χρόνῳ πολλῷ δι᾽ ἀρετῆς καθαρθεῖσαι παντάπασι θεότητος μετέσχον: but to these a third, that also from Plutarch (De Isid. et Osir. 22), may be added. In all of these it expresses, in agreement with the view here asserted, Godhead in the absolute sense, or at all events in as absolute a sense as the heathen could conceive it. Θειότης is a very much commoner word; and its employment everywhere bears out the distinction here drawn. There is ever a manifestation of the divine, of some divine attributes, in that to which θειότης is attributed, but never absolute essential Deity. Thus Lucian (De Cal. 17) attributes θειότης to Hephaestion, when after his death Alexander would have raised him to the rank of a god; and Plutarch speaks of the θειότης τῆς ψυχῆς, De Plac. Phil. v. 1; cf. De Is. et Os. 2; Sull. 6; with various other passages to the like effect.
It may be observed, in conclusion, that whether this distinction was intended, as I am fully persuaded it was, by St. Paul or not, it established itself firmly in the later theological language of the Church—the Greek Fathers using never θειότης, but always θεότης, as alone adequately expressing the essential Godhead of the Three several Persons in the Holy Trinity.
Although not focused lexically, I'd still quote one of the Church fathers on Col 2:9, using the Catena Bible site.
Ambrose of Milan AD 397
The law has proved God’s oneness. It speaks of one God, as also the apostle when he says of Christ: “In whom dwells all the fullness of the Godhead bodily.” For if, as the apostle says, all the fullness of the Godhead, bodily, is in Christ, then must the Father and the Son be confessed to be of one Godhead. Or if one desired to sunder the Godhead of the Son from the Godhead of the Father, as long as the Son possesses all the fullness of the Godhead bodily, what is supposed to be further reserved, seeing that nothing remains over and above the fullness of perfection? Therefore the Godhead is one.