Introduction
Luke has many themes, universalism, women, poor/rich, possessions, outcast, salvation, Gentiles, Son of Man, Holy Spirit, families, households, hiddenness, repentance, prayer, sinners.... These are easy to find with a concordance. More easily overlooked is the reversal theme in Luke.
Luke writes in part to remind us that life doesn't always come out like you expect. Murphy's law.

I. The reversal element in Luke can be seen--in Jesus' birth and childhood.

1:46-55, esp. 51-53.
The message to shepherds.
Fathers, 2:48-50.

II. The reversal element in Luke can be seen--in Jesus' early ministry.

Humble beginnings, 3:1-3.
John the Baptist, quoting Isaiah, 3:4ff.
Repentance theme.
Isaiah quotation, 4:18ff.
Beatitudes, 6:20ff.
Pharisee and sinful woman, 7:36ff.

III. The reversal element in Luke can be seen--in Jesus' teachings

Beelzebub, 11:23.
Narrow door, 13:30.

IV. The reversal element in Luke can be seen--in Jesus' parables and ministry

Good Samaritan, 10:25ff.
Mary and Martha, at least a contrast theme, 10:38.
Rich fool, 12:15ff.
Wedding feast, 14:11.
Prodigal son, 15.
Rich man and Lazarus, 16:19ff.
Ten lepers, 17:11ff.
Pharisee/tax collector, 18:9ff, esp. v. 14.
Rich ruler, 18:18ff, esp. V. 29-30.

Conclusion
There are many other passages, other evidences, of the upside-down nature of Christianity. In Luke's gospel one might also point to the hiddenness/opening theme, Jesus is the one who open minds, understand, eyes, and the Scriptures. You can find many more reversal accounts on your own as you read through Luke's gospel. The great reversal of the gospels is the resurrection of Jesus. The resurrection is the promise of what is possible in your life and my life. Jesus' followers went forth, and according to Luke's testimony, continued to turn the world upside down. So can we.