“Strain” means “passage of song or poetry” (OED); the implication is that Medea is casting a spell on the stars, the spell being in the form of a song or chant. Both Ovid and Seneca present Medea as having (or claiming to have) power over the heavens. First, Ovid:
“O Night, most faithful to these my mysteries, and ye golden Stars, who, with the Moon, succeed the fires of the day, and thou, three-faced Hecate, who comest conscious of my design, and ye charms and arts of the enchanters, and thou, too, Earth, that dost furnish the enchanters with powerful herbs; ye breezes, too, and winds, mountains, rivers, and lakes, and all ye Deities of the groves, and all ye Gods of night, attend here; through whose aid, whenever I will, the rivers run back from their astonished banks to their sources, and by my charms I calm the troubled sea, and rouse it when calm; I disperse the clouds, and I bring clouds upon the Earth; I both allay the winds, and I raise them; and I break the jaws of serpents with my words and my spells; I move, too, the solid rocks, and the oaks torn up with their own native earth, and the forests as well. I command the mountains, too, to quake, and the Earth to groan, and the ghosts to come forth from their tombs. Thee, too, O Moon, do I draw down, although the Temesæan brass* relieves thy pangs. By my spells, also, the chariot of my grandsire† is rendered pale; Aurora,‡ too, is pale through my enchantments.”
Publius Ovidius Naso (8 CE). Metamorphoses 7.192–209. Translated by Henry T. Riley (1893). Project Gutenberg.
* Temesa in Etruria was famous for its copper mines. † Medea was the daughter of Aeëtes, king of Colchis, who was the son of Helios, the sun-god. ‡ The goddess of the dawn.
Note that this is the spell that Medea casts to rejuvenate Aeson, king of Iolcus, after first cutting his throat. Pope has already alluded to this story:
When Dulness, smiling—“Thus revive the Wits!
But murder first, and mince them all to bits;
As erst Medea (cruel, so to save!)
A new Edition of old Æson gave,
Alexander Pope (1743). The Dunciad, book 4, lines 119–122. Wikisource.
Second, Seneca:
Medea At my command the sun and stars together shine,
The heavenly law reversed; while in the Arctic sea
The Bears have plunged.* The seasons, too, obey my will:
I’ve made the burning summer blossom as the spring,
And hoary winter autumn’s golden harvests bear.
The Phasis† sends his swirling waves to seek their source,
And Ister,‡ flowing to the sea with many mouths,
His eager water checks and sluggish rolls along.
The billows roar, the mad sea rages, though the winds
All silent lie. At my command primeval groves
Have lost their shade; the sun, abandoning the day,
Has stood in middle heaven; while falling Hyades§
Attest my charms.
Lucius Annaeus Seneca the Younger (c. 50 CE). Medea 4.757–769. Translated by Frank Justus Miller (1907). Project Gutenberg.
* The constellations Ursa Major (the great bear) and Ursa Minor (the little bear) always remain above the horizon, as seen from Europe. † The river Rioni, in the Caucasus. ‡ The river Danube. § A star cluster in the constellation Taurus.
