The Hebrew word most often translated as "body" or "flesh" is בּשׂר (basar) and is Strong's #1320. The first time the word is used in Scripture is when G-d takes a rib out of Adam's side and closes up his flesh:
So the LORD G-d caused a deep sleep to fall upon the man, and he slept; then He took one of his ribs and closed up the flesh at that place. (Genesis 2:21)
The Septuagint translates basar into Greek as σαρκα (sarxa- Strong's #4561) which is usually translated into English as "flesh". It is used 149 times in 126 verses of the Greek Scriptures.
The Greek word for "body" from the Greek Scriptures is σωμα (soma- Strong's #4983). The first time this word is used is in Matthew when the Master tells us that it is better to lose one part of our body than to burn in Gehenna:
"If your right eye makes you stumble, tear it out and throw it from you; for it is better for you to lose one of the parts of your body, than for your whole body to be thrown into hell." (Matthew 5:29)
In these words and the related passages of Scripture we can see the clear meaning of body... our physical form- our flesh. We have a material nature that we share with other creatures. We eat and drink to sustain those physical bodies in a manner similar to plants and animals.
Scripture makes additional distinctions between the flesh of humans, animals, birds, and fish:
All flesh is not the same flesh, but there is one flesh of men, and another flesh of beasts, and another flesh of birds, and another of fish. (1 Corinthians 15:39)
In this passage, Paul makes an analogy using the differences between the flesh of men, beasts, birds, and fish to demonstrate the differences between the perishable physical body that dies and the imperishable physical body that will be raised at the resurrection of the dead. I find interesting that as lists the kinds of flesh he moves from the greater to the lesser from man down to fish. (In the same chapter, he uses the differences between the different kinds of celestial objects and lists them from greater to lesser in terms of brightness from the sun down to the stars). Is he indicating that the imperishable body is somehow less than the perishable? This seems to contradict his later statements that the perishable body was sown in dishonor but raised in honor and sown in weakness but raised in power thus esteeming the imperishable body. The reason he changed the order is uncertain.
Let's move on to soul...