Some of my favorite techniques for teaching abstract concepts is to draw upon prior knowledge and have students relate the information to their lives.
When teaching logic in the past, I've used the scene in Alice in Wonderland where one door always lies and the other always tells the truth.
I've also had students construct logical arguments to convince their parents they should be able to stay up all night or attend concerts. Or, on a more altruistic note, have them argue for public policy issues. When the end result of the logical argument is one they like, they quickly find a way to get there using the rules of logic.
Another activity, as dgraab suggests, is to give students the opportunity to send one another secret messages.
Authentic activities like these help students process these advanced concepts. I've added some links to logic puzzles and riddles in the resource section below. Enjoy!