Δόξαν δίωκε.
Pursue glory.
This is one of the maxims attributed to the Seven Sages as recorded by Stobaeus. The word δόξα has a wide range of meaning in Greek; the specific meaning of "glory" became important for Christianity, as in English doxology.
Ἔριν μίσει.
Hate strife.
Don't let μίσει fool you: that's the imperative form of an -εω contract verb! From the Greek root μίσ- we get English words like misanthrope and misogyny. Meanwhile, for more about strife personified as a goddess, Ἔρις, see Wikipedia: Eris.
Πάντα λίθον κινεῖν.
To move every stone.
Compare the English saying "to leave no stone unturned." The historian Joannes Zonaras marks this as a proverbial expression: πάντα λίθον κινῶν, τὸ τῆς παροιμίας (παροιμία = proverb), as does Nicephorus Gregoras, πάντα λίθον κινῶν, τὸ τοῦ λόγου. From the λίθ- root, we get words like lithography and neolithic in English.
Εὔχου δυνατά.
Pray for things that are possible.
The verb εὔχου is a middle imperative from the deponent verb εὔχομαι; like many middle verbs it can still take a direct object: δυνατά, an adjective being used here as a noun, "possible (things)." This is one of the maxims attributed by Stobaeus to the Seven Sages.
Κάθαμμα λύειν.
To loosen the knot.
As Erasmus explains, this is a reference to the legend of the Gordian knot, which you can read about also at Wikipedia. Alexander the Great famously cut the knot with his sword rather than figuring out how to untie it (see below). Compare this saying from an earlier blog post (in fact, the very first Greek proverb post at this blog!): Γόρδιος δεσμός.
And to finish up, here's a random proverb and a random LOLCat too: