What are the distinctive use of parables used in Luke's gospel using quotations?
There are many parables, or stories that convey a moral truth in Luke, around 20.
"Judge Not Lest You Be Judged" Luke 6:37-42
"He also told them this parable: "Can a blind man lead a blind man? Will they not both fall into a pit?  A student is not above his teacher, but everyone who is fully trained will be like his teacher.  "Why do you look at the speck of sawdust in your brother's eye and pay no attention to the plank in your own eye?" 
"Think Before You Act" Luke 14:28-33
"Suppose one of you wants to build a tower. Will he not first sit down and estimate the cost to see if he has enough money to complete it?  For if he lays the foundation and is not able to finish it, everyone who sees it will ridicule him,  saying, `This fellow began to build and was not able to finish.'" 
"Help The Poor And God Will Bless You" Luke 14:12-14
 "Then Jesus said to his host, "When you give a luncheon or dinner, do not invite your friends, your brothers or relatives, or your rich neighbors; if you do, they may invite you back and so you will be repaid."
"The Prodigal Son" Luke 15:29 11-32
 " `My son,' the father said, `you are always with me, and everything I have is yours.  But we had to celebrate and be glad, because this brother of yours was dead and is alive again; he was lost and is found.'"