How do people who reject transubstantiation interpret these verses? Luke 22:19 (The Message)


  Taking bread, he blessed it, broke it, and gave it to them, saying,
  “This is my body, given for you. Eat it in my memory.”


It has been argued that even the grammar must be taken into account. From the grammatical structure of the sentence is the meaning of transubstantiation derived. The verse in Luke has been used to defend the doctrine of transubstantiation, but what about the next verse of John? Apparently, Jesus really emphasizes the fact that he is a piece of food, waiting to be eaten. How can this not be seen as transubstantiation? Maybe it's metaphorical, but still, he describes himself in a similar way.

John 6:35-40 (New International Version)


  Then Jesus declared, “I am the bread of life. Whoever comes to me will
  never go hungry, and whoever believes in me will never be thirsty. But
  as I told you, you have seen me and still you do not believe. All
  those the Father gives me will come to me, and whoever comes to me I
  will never drive away. For I have come down from heaven not to do my
  will but to do the will of him who sent me. And this is the will of
  him who sent me, that I shall lose none of all those he has given me,
  but raise them up at the last day. For my Father’s will is that
  everyone who looks to the Son and believes in him shall have eternal
  life, and I will raise them up at the last day.”


Now, this part seems to get a bit eerie. As it is a piece of dialogue in literature, it illustrates Jesus' character and how he reacts to questions. When prompted by the "Jews", he appears to take the bread as body of Christ literally, which may support the doctrine of transubstantiation. 

John 6:52-59 (New International Version)


  Then the Jews began to argue sharply among themselves, “How can this
  man give us his flesh to eat?”
  
  Jesus said to them, “Very truly I tell you, unless you eat the flesh
  of the Son of Man and drink his blood, you have no life in you.
  Whoever eats my flesh and drinks my blood has eternal life, and I will
  raise them up at the last day. For my flesh is real food and my blood
  is real drink. Whoever eats my flesh and drinks my blood remains in
  me, and I in them. Just as the living Father sent me and I live
  because of the Father, so the one who feeds on me will live because of
  me. This is the bread that came down from heaven. Your ancestors ate
  manna and died, but whoever feeds on this bread will live forever.” He
  said this while teaching in the synagogue in Capernaum.


How do people who reject transubstantiation (but believe in sola scriptura) interpret these verses and still refute transubstantiation?
Side note: The issue isn't really about the doctrine of sola scriptura, but rather about literalism. "Sola scriptura" is a term used by Protestants to mean that we believe scripture is the only ultimate authority, as opposed to Catholic doctrines that the teachings of the Church fathers have equivalent or comparable authority to scripture. But nothing in your question is contrasting a Bible quote to a quote from a Church father. Rather you seem to be saying, "How can someone take the Bible literally and not believe in trans-substantiation?" But anyway, to the point ...

The easy answer is that people who do not believe in trans-substantiation believe that Jesus was not speaking literally, but symbolically or metaphorically.

When I say that I take the Bible literally, I do not mean that literally! Of course the Bible includes many statements that are poetic, symbolic, and so on. Like when I read Isaiah 55:12, "The mountains and the hills Shall break forth into singing before you, And all the trees of the field shall clap their hands", I don't suppose that he means that trees will literally sprout hands and applaud. This is poetic language to describe a joyous day. When people say that we take the Bible literally, we mean that we read the Bible the same way we read any other book: If a statement is presented as describing actual human beings doing things in the real world, then we accept that the writer is trying to say that these actual human beings did these actual things, even if those things are incredible, such as a miracle. We don't mean that we insist that anything that sounds like poetry or metaphor must be a literal physical description. (And yes, we concede the possibility that there may be cases where it is not obvious whether something is intended literally or figuratively. But we insist that's relatively rare. But that's another subject.)

So perhaps more relevantly, Matthew 16:6 "Then Jesus said to them, “Take heed and beware of the leaven of the Pharisees and the Sadducees.” The text goes on how the disciples wondered what he was talking about, Jesus explains, and it concludes, verse 12, "Then they understood that He did not tell them to beware of the leaven of bread, but of the doctrine of the Pharisees and Sadducees."

So when Jesus talked about the "leaven of the Pharisees", he was speaking poetically. He was not talking about literal leaven, but using the word leaven as a symbol for their teaching.

Likewise, people who are literalists and who reject trans-substantiation say that when Jesus talked about eating his body and drinking his blood, that he was speaking metaphorically, not literally. Just like when he talked about the leaven of the Pharisees.

I think most literalists would say that it is clear that Jesus was speaking symbolically here because at the time he said, for example, "This is my body which is broken for you", it is clear that the bread was not literally his physical body, as he was sitting right there. When we celebrate the eucharist today, I don't think anyone would suppose that a chemical test of the bread and wine would show it to be literal meat and blood from a human being. So when a trans-substantiationist says that Jesus meant these words literally, he doesn't really mean literally either. He doesn't think that the bread and wine are literally meat hacked out of Jesus's dead body and blood drained from his veins. He means that it becomes the body and blood of Jesus in some mystical, spiritual sense. So, in my humble opinion, the two camps are really not that far apart. Not that this hasn't resulted in a lot of argument.