...which one is the easiest to teach a new player?

I would say Warhammer Invasion, simply because there is really only one icon that new players have to keep track of and that icon works for everything.

Warhammer is the easiest to teach, but I think the other two may be a bit more fun depending on what kind of player you and they are. I like all three. CoC is fun in its weirdness, Warhammer in its numerous branching decision tree, and Thrones because of the open ended strategical though it requires.

Mechanically how are each different?

All 3 games are quite different. You'd likely get a better picture of how they differ mechanically from watching the demo videos than from anything we could tell you.

The new LOTR LCG is really easy to pick up and learn. I've only played WH:I other than that, and I'd say its easier than that. Part of it is you're playing against a deck instead of against each other (and the enemy deck is pretty easy to run), and the starter set has fewer player cards so its easy to learn them, though I think the game is also fantastically fun.