Cheat:

 Here are the combinations for the invaders who are otherwise
 unavailable.
 When collecting bodies:

 - Invite a merchant and a pirate : a pesky little carpenter will come
   with them
 - Invite a general and a wizard : an annoying messenger comes with
   them
 - Invite a magic doll and a psychic : a curious little alien tags
   along
 - Invite a gem guard and a swordsman : a witch comes along with them