What happens to "usable once only" cards when Illusion is played?
I don't have an official ruling to cite, but my interpretation would be that Illusion only removes the monster and any Monster Enhancers specific to that monster, but does not affect any one-shot items or other "&pm;X to either side" cards.

What's confusing here is that, instead of using the standard term "Monster Enhancer" (like, say, the Mate card does), the Illusion card text just says to discard "any cards that have been played to modify [the monster]".  However, as far as I can tell, these two terms as effectively synonymous; the rules essentially define a Monster Enhancer as any card played to modify an individual monster:


  Monster Enhancers
  
  Certain cards, called monster enhancers, raise or lower the combat strength of individual monsters. (Yes, you can have a negative enhancement.) Monster enhancers may be played by any player during any combat.
  
  All enhancers on a single monster add together. If there are multiple monsters in a combat, the person who plays each enhancer must choose which monster it applies to. Exception: Anything that enhances a monster also enhances its Mate &hellip; if Ancient, Enraged, and Mate are played on a single monster, in any order, you are facing an Ancient Enraged monster and its Ancient Enraged Mate. Good luck &hellip; 


(The Mate card text was changed to explicitly refer to Monster Enhancers in The Great 2010 Changeover; I suspect that the lack of a similar change to the Illusion card may have been an oversight.)

The essential difference between Monster Enhancers and one-shot items is that Monster Enchancers modify a specific monster (and possibly its Mate, per the explicit exception quoted above), whereas one-shot items add a bonus to a side in combat.

In particular, if there are multiple monsters involved in a combat (e.g. due to Wandering Monster cards being played), a one-shot item granting a bonus to the monsters' side will not be tied to any specific monster, and will not disappear even if some of the monsters are subsequently removed from combat by any means.

Of course, if all the monsters leave combat with no replacement (and no new wandering monsters appear within the rules-prescribed 2.6 seconds), then the combat is over and any bonuses of any kind become irrelevant.