κύκνειος ~ κυκνείου (adj. masc.): of a swan
ὄϊς ~ ὄϊος (noun c.): sheep
κύων ~ κυνὸς (noun c.): dog
αἴξ ~ αἰγός (noun c.): goat
κάμηλος ~ καμήλου (noun c.): camel
These are the proverbs (and there are always more proverbs at the blog):
Κύκνειον ᾆσμα.
Τῷ λύκῳ τὴν ὄϊν.
Ἐν φρέατι κυνομαχεῖν.
Ἀτενὲς ὁρᾷς ὥσπερ ἡ αἲξ τὴν θάλασσαν.
Κάμηλος καὶ ψωριῶσα πολλῶν ὄνων ἀνατίθεται φορτία.
And now, some commentary:
Κύκνειον ᾆσμα.
A swan song.
You've seen another version of this saying in a previous post: Κύκνειον μέλος. The legend of the song that the swan (supposedly) sings just before it dies, having spent the rest of its life in silence, has its own article at Wikipedia: Swan song. The word ᾆσμα is from the verb ἀείδω, "sing," while μέλος has a more general meaning: it is a "part" or "limb" of a larger whole, and then comes to mean specifically a "tune" or "song."
Τῷ λύκῳ τὴν ὄϊν.
(Entrusting) the sheep to the wolf.
Of course this is not a good idea! Compare the English saying, "Setting the fox to guard the henhouse." For more Greek and Latin parallels, see Erasmus.
Ἐν φρέατι κυνομαχεῖν.
To fight with dogs in a well.
This is definitely something you want to avoid! A dog-fight is bad enough, but it is even more violent and dangerous if it is happening in a confined space like a well. You can also read more about this Greek saying in Erasmus.
Ἀτενὲς ὁρᾷς ὥσπερ ἡ αἲξ τὴν θάλασσαν.
You are gazing intently like the goat at the sea.
You've seen an abbreviated version of this saying in a previous post: Αἲξ θάλασσαν. The idea is that the goat is amazed by the sea, and looks at it with fascination because it is something entirely new. Goats live in mountains and valleys; they do not often get to see the sea, so the saying is used to refer to someone who is staring in amazement at something they have not seen before.
Κάμηλος καὶ ψωριῶσα πολλῶν ὄνων ἀνατίθεται φορτία.
A camel, even a mangy one, can bear the loads of many donkeys.
The idea is that someone who is superior can still continue to excel even when they are not in top condition. Of course a camel can carry more than multiple donkeys, and that is still true even when the camel is mangy: καὶ ψωριῶσα (the καὶ is adverbial).
And here's a random proverb and a random LOLCat too: