Basically, when you kill a slayer you release the door in the slayer's area, allowing you to leave. So...
SW area:
Click here to view the secret text
×Just kill the slayer with the decoy.
SE area:
Click here to view the secret text
×You could do it easily with the speed potion, but I don't think you can get enough distance on the slayer.
Click here to view the secret text
×But remember what happens if you have a sword and turn on hot tiles.
Click here to view the secret text
×Or rather, what doesn't happen.
N area:
Click here to view the secret text
×There doesn't seem to be anything that can help you, does there?
Click here to view the secret text
×Try right-clicking on the Slayer, that should give you an idea.