Wordsworth thought that the phrase was a leap of pure imagination:
Here is the full strength of the imagination involved in the word, hangs, and exerted upon the whole image: First, the Fleet, an aggregate of many Ships, is represented as one mighty Person, whose track, we know and feel, is upon the waters; but, taking advantage of its appearance to the senses, the Poet dares to represent it as hanging in the clouds, both for the gratification of the mind in contemplating the image itself, and in reference to the motion and appearance of the sublime object to which it is compared.
William Wordsworth (1815). Poems, preface to volume I, pp. xxii–xxiii. London: Longman.
But to me Milton’s description suggests a Fata Morgana, a form of atmospheric distortion—a kind of superior mirage—that can form multiple images of objects close to the horizon. The images are stacked vertically and some may be inverted.
Occasionally, in the western extremity of the Mediterranean, where the sea narrows as it approaches the straits, lofty arches of clouds, extending from Spain to Africa, span the flood like the roof of a huge vault. Upon the surface of this roof, a traveller, returning from the East, beheld an extraordinary picture, painted by means identical, probably, with those which, in the neighbourhood of Scylla and Charybdis, give fleeting existence to the Fata Morgana, of which I shall presently speak. From the ship’s deck on which he stood, the traveller, looking westward, saw in the clouds a fleet in full sail, though with the hulls upward, and the masts and rigging pointing to the sea
Anon (1868). ‘Pictures in the Clouds’. In Chambers’s Journal, 26 December 1868, p. 821.
Wikipedia has various photos showing the phenomenon: in the one below, there are three distinct horizontal bands just above the horizon, giving the impression of a cloudy or misty background (but actually consisting of three images of the sea surface), against which three images of a boat can be seen, the middle image being inverted, thus appearing to “hang in the clouds” in the manner described by Milton.

‘Brocken Inaglory’ (2008). ‘Superior mirage of a small boat’. CC-BY-SA.
But could Milton have known about the ‘Fata Morgana’ phenomenon? As noted in ‘Pictures in the Clouds’, the phenomenon was particularly common in the Straits of Messina (“the neighbourhood of Scylla and Charybdis” as the writer puts it). Accordingly, a number of early writers on the phenomenon were Italian, most notably Ignatio Angelucci:
La mattina dell’ Assontione della Beatissima Vergine, standomi solo alla fenestra, viddi cose tant, e tanto nuove che di ripensarle non mai satio, estanco. […] Il Mare, che bagna la Sicilia si gonfiò, e diventò per dieci miglia in circa di lunghezza, come una spina dimontagna nera; e questo della Calabria spianò, e comparve in un momento un cristallo chiarissimo, e trasparente che parea uno specchio, che con la cima appoggiasse su quella montagna di acqua, e col piede al Lido di Calabria. In questo Specchio comparve subito di colore chiaro oscuro une fila di più di 10000. Pilastri d’uguale larghezza, e altezza, tutti equidistanti, e di un medesimo vivessimo chiarore, come di una medesima ombratura erano gli sfondati frà pilastro e pilastro. In un momento poi i pilastri si smezzarono d’altzza, e si arcuarono in forma di cotesti aquedotti di Roma, ò delle sustruttioni di Salome; e restò semplice specchio il resto dell’ acqua, sino all’ acqua ammontonata di Sicilia: mà per poco, che tosto sopra l’arcata si formò un gran cornicione: frà poco sopra del cornitione si sormarono castelli reali in quantità, disposti in quella vastissima piazza di vetro, e tutti di una forma, e la voro: frà poco, deili castelli rimasero quantità di torri tutte uguali: frà poco le torri si cambiarono in teatro di colonnati: frà poco il teatro si stese, e secene una doppia fuga: frà, poco la fuga de colonnati diventò lunghissima facciata di fenestre in dieci fila: della facciata si sè varieta di selue di pini, e cipressi eguali, e d’altre varietà d’arbori. E qui il tutto disparue, e’l mare con un poco di vento ritornò mare. Questa è quella Fata Morgana, che ventisei anni ho stimata inverisimile.
On the fifteenth of August, 1643, as I stood at my window, I was surprised with a most wonderful, delectable vision. The sea that washes the Sicilian shore swelled up, and became, for ten miles in length, like a chain of dark mountains; while the waters near our Calabrian coast grew quite smooth, and in an instant appeared as one clear polished mirror, reclining against the aforesaid ridge. On this glass was depicted, in chiaro scuro, a string of several thousands of pilasters, all equal in altitude, distance, and degree of light and shade. In a moment they lost half their height, and bent into arcades, like Roman aqueducts. A long cornice was next formed on the top, and above it rose castles innumerable, all perfectly alike. These soon split into towers, which were shortly after lost in colonnades, then windows, and at last ended in pines, cypresses, and other trees, even and similar. This is the Fata Morgana, which, for twenty-six years, I had thought a mere fable.
Ignatio Angelucci. Letter of 22 August 1643. Quoted in Athanasius Kircher (1671). Ars Magna Lucis et Umbrae. p. 704–705. Translated by Henry Swinburne, Travels in the Two Sicilies, pp. 264–265.
Milton was fluent in Latin and Italian, and had travelled in Italy, so that he could have learned of the phenomenon there, or read a description in de Ferrariis:
Quandoque figurae nubium, sunt quae Navium, et velorum simulachra reddunt: ubi nulla est classis. Haec Phasmata non solum in expertos fefellerunt. Non diu est quod tota ora quae est ab Hydrunto
ad Garganum Montem, una et eadem hora ante ortum solis vidit classem ab Orientis parte velificantem, creditum est Turcarum illam fuisse, et antequam Phasma, seu illa delusio albicante Aurora detegeretur variae huc atque illuc literae scriptae sunt, ac missi Nuntii de adventu ingentis Classis. Hoc fortasse modo, aut altero, quem diximus, ut credo, à Lilybeo vidit nescio quis classem e portu Carthaginis exeuntem.
And as these figures are of mists, they give likenesses of ships and sails, where there is no fleet. These apparitions deceive not only the inexperienced. It is not long since the whole coast, from Hydrunto* to Monte Gargano, at one and the same hour before sunrise, saw a fleet sailing from the east. It was thought to have been that of the Turks,† and before that specter or delusion was revealed by the lightening dawn, various letters were composed here and there and messengers were sent concerning the approach of this imposing fleet. Perhaps in this way or another of which we shall speak, as I believe, someone (I don’t know who) from Lilibeo‡ saw a fleet leaving the port of Carthage.
Antonio de Ferrariis (1558). Liber de situ Iapygiae. Translated by Andrew T. Young.
* Otranto † The Ottomans had recently (1480) sacked Otranto ‡ Marsala
Another poetic evocation of the Fata Morgana appears in Tennyson’s Idylls of the King, appropriately enough, since Morgana (Morgan le Fay) is a character in Arthurian mythology:
Then that old Seer made answer playing on him
And saying, “Son, I have seen the good ship sail
Keel upward, and mast downward, in the heavens,
And solid turrets topsy-turvy in air”
Alfred Tennyson (1872). Gareth and Lynette, p. 18. London: Strahan.