Ἀτρέως ὄμματα.
The eyes of Atreus.
This refers to someone with a cruel look, like the wicked Atreus who tricked his twin brother, Thyestes, into eating his own sons in a stew. When Thyestes was done eating, Atreus then brought out the dead boys' hands and feet to reveal their identities (see medieval illustration below). Agamemnon and Thyestes are the sons of Atreus, i.e. Atreides. Find out more at Wikipedia: Atreus.
Βασιλεῖ νόμος ἄγραφος.
For the king, the law (is) not written.
In other words, the law does not apply to the king. There is a fuller form of this proverb also: Μωρῷ καὶ βασιλεῖ νόμος ἄγραφος, in which the fool, μωρός, like the king, is outside the rule of the written law. The Greek word νόμος gives us the English words with -mony as a suffix, like economy, astronomy, etc. And, yes, the plant "basil" does get its name from Greek βασιλεύς; it is βασιλικόν φυτόν, the royal plant.
Αἲξ Σκυρία.
A Scyrian goat.
The she-goats from the island of Skyros in Greece were proverbial for kicking over the milk bucket after they had been milked. As such, they came to stand for someone who was contrary and troublesome, squandering their own riches and resources for no good reason.
Ἐξ ἑνὸς πάνθ᾽ ὁρᾷν.
To see all things from the one.
The saying appears in the sayings collected by Apostolius. The word πάντα, "all (things)," drops its final vowel before the following vowel, and the rough breathing causes the aspiration: πάνθ᾽ ὁρᾶν. Compare the opposite idea expressed in the U.S. motto: E pluribus unum, "Out of the many, one."
Ὗς ὀρίνει.
The boar provokes (trouble).
This pithy little Greek saying is a bit hard to translate into English without an explicit object for the verb. The idea is that a boar or wild pig is like a violent or argumentative person who stirs things up, causing trouble. The word ὗς can refer either to a wild pig or a domesticated pig.
And to finish up, here's a random proverb and a random LOLCat too: