In Book 1, Milton uses allusions and simile to convey Satan's enormous stature and power:
Thus Satan talking to his nearest mate
With head up-lift above the wave, and eyes
That sparkling blaz'd, his other parts besides
Prone on the flood, extended long and large
Lay floating many a rood, in bulk as huge
As whom the fables name of monstrous size,
Titanian, or Earth-born, that warr'd on Jove,
Briareos or Typhon, whom the Den
By ancient Tarsus held, or that sea-beast
Leviathan, which God of all his works
Created hugest that swim th' ocean stream...
Milton is referring to monsters and villains from Greek and Roman mythology: Titans (Titanian) and Giants (Briareos or Typhon) confined to hell (Tarsus) after rebelling against Jove (the king of the gods)—both portrayed as enormous, violent beings; the Leviathan is a Biblical sea-creature described in the Book of Job.
By comparing Satan to these notorious creatures—all of whom defied the gods or God, just as Satan has defied God—Milton is emphasizing the gravity of Satan's decision, while also carving out a place for Satan in a canon of mythological figures: insisting on his own power and notoriety, even though he has been banished to Hell. (Arguably, his banishment has only augmented his power.)
In Book 4, Milton uses a series of allusions to describe Eden/Paradise:
Not that fair field
Of Enna, where Prosérpine gath’ring flow’rs
Herself a fairer flow’r by gloomy Dis
Was gathered, which cost Ceres all that pain
To seek her through the world; nor that sweet grove
Of Daphne by Orontes, and th’ inspired
Castalian spring, might with this Paradise
Of Eden strive...
Milton is naming a number of other paradises or classical locations renowned for their beauty and tranquility: Enna (from Roman mythology), where Persephone lived before being kidnapped by Pluto/Hades and led to the Underworld; the "grove" of the nymph Daphne (Greek mythology); and the Castalian Spring, an oasis near the Delphic Oracle (Greek mythology). Yet none of these, he says, can compare to Eden—in order to draw attention to the specifically biblical, Judeo-Christian origins of the narrative at hand (as opposed to Pagan classical mythology) and to pointedly emphasize Eden's outsized, nearly unfathomable beauty: all other well-known paradises pale in comparison.
Milton employs this technique several times throughout the poem—emphasizing the beauty or magnitude of a character, object, or land by explicitly comparing it to similar references from classical mythology, which he insists look far worse in comparison. These references would have been familiar to readers of his era, and thus, his comparisons would have seemed especially bold, provocative, and striking—demonstrating to the reader that the Paradise they are encountering in the poem is unlike any other.
In Book 4, Milton describes the good angels preparing to battle Satan after he has been discovered in Paradise, and employs an allusion and a simile to describe them:
While thus he spake, th’ angelic squadron bright
Turned fiery red, sharp’ning in moonèd horns
Their phalanx, and began to hem him round
With ported spears, as thick as when a field
Of Ceres ripe for harvest waving bends
Her bearded grove of ears, which way the wind
Sways them; the careful ploughman doubting stands
Lest on the threshing floor his hopeful sheaves
Prove chaff.
Milton is comparing the throng of good angels to a field of corn or wheat (Ceres is the Roman god of agriculture, often represented with corn/wheat)—a fairly flimsy crop that is easily buffeted by the wind. Thus, the throng of angels is not really "thick" at all—but insubstantial and weak.
This may seem somewhat confusing, since Milton seems to implicitly support the good angels over Satan—yet they appear easily bested by him. But this also emphasizes the power of Satan's rage and rebelliousness (and the power of evil and corrupt authority in general): ultimately, the good angels are only able to defeat Satan after he has carried out his plot against Adam and Eve and thinks himself triumphant.
In Book 5, Adam awakes next to Eve in Eden, and their morning is described with rich imagery (as well as a few allusions):
Now Morn her rosy steps in th’ eastern clime
Advancing, sowed the earth with orient pearl,
When Adam waked, so customed, for his sleep
Was airy light, from pure digestion bred,
And temperate vapours bland, which th’ only sound,
Of leaves and fuming rills, Aurora’s fan,
Lightly dispersed, and the shrill matin song
Of birds on every bough; so much the more
His wonder was to find unwakened Eve
With tresses discomposed, and glowing cheek,
As through unquiet rest: he on his side
Leaning half-raised, with looks of cordial love
Hung over her enamoured, and beheld
Beauty, which whether waking or asleep,
Shot forth peculiar graces; then with voice
Mild, as when Zephyrus on Flora breathes,
Her hand soft touching, whispered thus.
This instance of imagery highlights both the transcendent beauty of Eden—which matches Eve's beauty, drawing a parallel between womankind and the natural world—and hints at the differences between Adam and Eve (in terms of both personality and social status): whereas Adam's sleep is "airy light," and he wakes up feeling calm, Eve has just had a dream in which Satan appeared to her and urged her to eat the forbidden fruit. Eve's tresses are "discomposed," suggesting her susceptibility and wildness—versus Adam's composure and leadership (he wakes up first, while Eve is still engrossed in her dream).
Milton also makes use of a few allusions to Greek poetry/mythology: the "rosy steps" of "Morn" are reminiscent of the "rosy-fingered dawn," an epithet that appears in the Illiad and the Odyssey, and Zephyrus is a Greek god of the west wind who is married to Flora (the goddess of flowers). These allusions further elevate the scene—underscoring the power of both Eden and Eve's beauty.
In Book 9, Milton uses a series of allusions to describe the serpent whose form Satan has assumed to seduce Eve:
So spake the Enemy of mankind, enclosed
In serpent, inmate bad, and toward Eve
Addressed his way [...]
Amidst his circling spires, that on the grass
Floated redundant: pleasing was his shape,
And lovely, never since of serpent kind
Lovelier, not those that in Illyria changed
Hermione and Cadmus, or the god
In Epidaurus; nor to which transformed Ammonian Jove,
or Capitoline was seen,
He with Olympias, this with her who bore Scipio the heighth of Rome.
Milton compares Satan (in Serpent form) to a number of different serpents in Greek and Roman mythology: Hermione and Cadmus were a married couple who were cursed by being transformed into snakes; Epidaurus was a Greek city where the temple of the god Asclepius, who carries a serpent-entwined staff, was located; Scipio was a Roman soldier who was rumored to be a demi-god (fathered by Jove, who took the form of a serpent).
By stringing together these allusions—all of which concern serpents of mythological importance—Milton demonstrates to the reader just how "lovely" and impressive Satan is as a serpent, and offers a justification for Eve's seduction: Satan is alluring in serpent form.