Ἐς κόρακας.
To the crows.
This is an insult: the crows are the crows who feed on the corpses at public executions. So, the idea is to "go hang yourself" — and then the crows will come feast. You can see the phrase used in Aristophanes' Peace.
Συβαριτικὴ τράπεζα.
A Sybaritic table.
This saying referred to an opulent, or exceedingly opulent, banquet table, as Sybaris was one of the wealthiest Greek colonies. It was located on the Italian coast in what is now the region of Calabria; you can find out more at Wikipedia: Sybaris, which includes a section on its cultural legacy.
Ἀπὸ τοῦ ἡλίου μετάστηθι.
Move out of the sunshine.
These are the words famously spoken by the Cynic philosopher Diogenes to Alexander the Great, as reported by Plutarch in his Life of Alexander. Alexander was curious to meet Diogenes and was eager to do him a favor. He found Diogenes lying in the sunshine; all Diogenes wanted from Alexander was for him to stop blocking his sunshine. This famous anecdote has its own Wikipedia article: Diogenes and Alexander.
Ἴδια φύλαττε.
Protect what is yours.
This is one of the Delphic maxims recorded by Stobaeus. The form φύλαττε is Attic; the dictionary form of the verb is φυλάσσω. And yes, English "idiot" is from Greek ἴδιος; details at the Wiktionary.
Προμέρου κύνες.
The dogs of Promerus.
This saying alludes to the legendary death of the playwright Euripdes: as Erasmus explains, Euripides was supposedly torn to pieces by the dogs of Promerus, a royal official who had conceived an enormous hatred for him. Promerus ordered the dogs to attack Euripides, and they did so. Aulus Gellius also reports that Euripides was killed by dogs, although he does not mention the name Promerus.
And to finish up, here's a random proverb and a random LOLCat too: