Proposed Canon
- Temporarily add and remove "natural" magic and abilities from units. (such as the ability to Move through the air from flyers) LIAB 33b
 Known Weirdomancers
As of yet, no known Weirdomancer has been introduced.
In simplest form this could be increasing rate of movement, and reduced or eliminated penalties for any Terrain Type, possibly including moving through walls. These would also fit the name since a unit that could move twice as fast as it should straight up a mountainside and through the walls of a city would be weird.
Conversely, it could also reduce movement and increase movement penalties for a side's enemies, with similar combat applications.
It is also possible that at a higher level this magic can perform ultimate movement tricks such as teleports which put the target unit in a different numbered hex.
It would also be possible to summon units from a distance including other planes, but this does not fit with the only summon seen so far - the Summon Perfect Warlord Spell. Given that Weirdomancy is a Discipline of Spookism, it's possible that a high level Weirdomancer can summon "spooks" (which might be ghosts or spirits) from the City of Heroes.
It is unknown how the portal to the magic kingdom works but it would fit with this suggested version of weirdomancy. That might mean a weirdomancer could create portals, possibly between locations in Erfworld, or to other dimensions such as Stupidworld, or the realms of the croaked or the daemons. An artifact that allowed access to and control of daemons would provide a symmetry to the Arkendish attuned to Charlie and its control of Archons.
 Real World
The Museum of the Weird contains Wax Figures (which would be Dollamancy), but also Monsters, Shrunken Heads, Freaks of Nature, and Giant Lizards. It also contains Mythical creatures such as the Fiji Mermaid and Bigfoot. Supernatural figures such as Vampires, Mummies, Werewolves and Ghosts are also covered. Generally, Wierd things include all that is Unexplained. It would not be surprising if Weirdomancy includes these things.
"Weird" has also been used to describe witches, warlocks, and sorcerers, so it is possible this is a broader discipline than has been shown in the stories so far.