What are Montresor's verbal and non-verbal strategies of initially engaging Fortunato and then luring him along throughout the story "The Cask of...

Montresor tricks Fortunato into coming into the crypt by using reverse psychology on him and trying to keep him at ease.

Montresor’s main strategy is to pretend that he does not want Fortunato to come see the wine.  First he implies that it would be better to let someone else look at it.  Then he continually inquires about Fortunato’s health, implying that he is too ill to remain.  He makes jokes to prevent Fortunato from knowing what is happening, and indeed the victim has no idea until he is already in the wall.

The first non-verbal cue Montresor gives Fortunato is shaking his hand.  He makes him think that he is happy to see him because they are friends. The reality is that he is happy to see him because he has a carefully orchestrated plan to kill him.  It would be a shame to let such a plan go to waste.  Fortunato is drunk, because of the Carnival.  His guard is down.

Montresor tells Fortunato that he has a special cask of wine that he needs an opinion on.  He knows that if he tells Fortunato that someone else will look at it, Fortunato will not be able to resist.  He also pretends to worry about Fortunato’s cold, so that the man will not realize how badly he wants him to go underground.

"My friend, no. It is not the engagement, but the severe cold with which I perceive you are afflicted. The vaults are insufferably damp. They are encrusted with nitre."

"Let us go, nevertheless. The cold is merely nothing. Amontillado! You have been imposed upon. And as for Luchresi, he cannot distinguish Sherry from Amontillado."

Montresor succeeds in getting Fortunato underground.  Once there, he uses a combination of verbal and nonverbal cues.  He jokes about being a member of the Masons, a secret society, and shows Fortunato the trowel.

"You? Impossible! A mason?"

"A mason," I replied.

"A sign," he said, "a sign."

"It is this," I answered, producing from beneath the folds of my roquelaire a trowel.

"You jest," he exclaimed, recoiling a few paces. "But let us proceed to the Amontillado."

The trowel gesture is designed to keep Fortunato at ease, making him think that everything is okay and it is all a joke.  It also explains away the presence of the trowel.  Montresor does not believe that Fortunato will question his having it now that he has shown it to him.  In fact, that is pretty much what happens.  Fortunato still thinks it is a joke until he is being bricked up in the wall.