Actually that is practical advice on effective non-violent forms of aggression against those who would wrong you. It's in the same vein as "Walk the extra mile" and "Turn the other cheek." Cultural and historical context is key to understanding what Jesus is proposing:
Judea is occupied territory, governed by foreign Romans with alien customs as well as corrupt Jews (Pharisees). Both factions are powerful enough to crush most forms of traditional resistance, typically physical violence and intellectual overpowering. Since resistance is still desired, how does a man effectively resist these powers without getting crushed in turn?
You know your enemy, and then use his own customs/spiritual nature against himself. The Romans were extremely proud and legalistic, having customs of respect versus disdain when slapping others and humanitarian laws severely punishing those who made locals carry their equipment for more than one mile. Resisting them physically assured you loss, but instead Jesus said to force those Romans who would abuse them to either slap them as an equal by turning their cheek just so or to stop slapping them, or to always carry their equipment more than a mile so as to invite punishment from their overseers or to make them stop making you carry their shit.
With the shirt and tunic (coat) part, that's subverting Jewish customs that inflicts a great deal of shame on a creditor for taking away your clothes and keeping it for more than a day. By making him look like a total asshole in the eyes of other Jews, one could make him stop abusing you by being overly generous and magnanimous in the face of his abusiveness.
This is not meekly inviting more abuses on oneself, of being a doormat. It's quite the opposite. It's presenting a terribly moral, cultural, and social dilemma on those who would abuse you that either makes them suffer consequences they would rather not suffer for harming you, or to stop harming you. It's highly aggressive and the equivalent of spiritual judo, requiring a deep knowledge and even respect of your enemies in order to be effective aPost too long. Click here to view the full text.