Abarim Publications' online Biblical Greek Dictionary
οστεον
The noun οστεον (osteon) means bone (hence our English word ossuary, or bone-box), and in the classics this word denotes particularly a single bone or cranium. In other words, where the noun σκελετος (skeletos) denotes a very dead but complete dead person, perhaps even a mummy, carefully preserved in a μνημα (mnema), meaning tomb or memorial (from the verb μναομαι, mnaomai, to remember), an οστεον (osteon) is an anonymous remnant of some person whose living σαρξ (sarx), flesh, has long disappeared and whose fundamental legacy has fallen apart, was carried off by animals and has become utterly and unrecognizably dispersed.
In the New Testament, our noun οστεον (osteon) is used 5 times — see full concordance — but strikingly, three of these occurrences describe the bones of the living Christ. This suggests that the elements of the hidden framework that keeps the Body of Christ together and gives it structure, may not always know and recognize each other. The Body of Christ is of course a mental creature, which consists of a great many disciplines in arts and sciences. And although practitioners of these disciplines may not always respect the others (not every mathematician also respects Shakespeare), it's common knowledge that all these disciplines support each other in the greater consilience of mankind's singular understanding of everything (compare Deuteronomy 6:4 with Hebrews 1:3 and Colossians 1:17).
The Hebrew word for bone(s) is גרם (gerem), from the verb גרם (garam), to leave over or save for later.
It's not clear where our noun οστεον (osteon) comes from, but possibly from a Proto-Indo-European term "hest", which has left traces in languages from Sanskrit to Persian to Celtic, all meaning bone. But what that PIE word originally may have meant isn't clear: what was a stray bone to very early humans? Or even the bones within one's living body? To the Greeks, the word οστεον (osteon) could also describe rocks that stuck out of the ground (earth's bony feet), or even the pits of fruits.
οστρακινος
The adjective οστρακινος (ostrakinos) means earthen, or made of baked clay (2 Corinthians 4:7 and 2 Timothy 2:20 only). It stems from the unused noun οστρακον (ostrakon), meaning earthen vessel or a shard of one. In Athens such earthen shards were used to cast votes with, particularly to have someone banished, which is where the words ostracism and ostracize come from. One of the gates of Jerusalem was called Potsherd Gate and was associated with Gehenna.
The noun οστρακον (ostrakon) could also describe the hard shells of snails, mussels and even turtles and eggs (the word οστρεον, ostreon means oyster, hence the word). Its origin is as obscure as that of the previous and traditionally these two words have been thought to derive from the same idea. Perhaps that idea was that bones relate to living flesh the way the earth relates to the heavens.