Well, it is 100% possible to order units to cast abilities. Simply, you could just base the abilities off of ones that are selectable in this area. Unfortunately, this would limit you gravely when it comes to trying to create many abilities.
Now that you've heard the bad news, let me tell you the good news. While you would be limited in choice for abilities to base the Pokemon's 'techniques' on, there is a method to get abilities to work even if they are based off of the same ability. Basically, you just have to put the abilities into a spellbook with a unique spellbook ID. Also, to avoid mess, it might be handy to put the techniques in a master spellbook. Anyway, that's optional, as there are 4 available slots down the bottom row.
As for getting the Neutral Units to cast these abilities, I want to know what your combat system is. Is it going to be turn by turn? If so, it would be advisable to base all offensive abilities off of an ability that creeps like to use. That way, they'd tend to cast them on their own accord (with any luck

). Otherwise, you could make new abilities for them. By this, I mean just recreate the abilities for them, only making the difference of basing them off of different abilities. This way, you'd be able to use triggers to order them to cast a random ability or just an ability depending on what Pokemon they are fighting against.
BTW, I am assuming that Pokemon have no attack (DUH, how else would you base a fighting system off of abilities?

). That way, you'd have an extra slot for an extra detail or something. However, I'd like for their to be abilities based off of the Moon Glaive ability (In other words, a dummy ability as Moon Glaive really does nothing as an ability, it functions as an upgrade) and make on for each type their is e.g. Ground, Fire, Flying... you get the picture. I think that somewhere along the lines you've already thought of this. That way, when it comes to having type advantages, you can just use a preset number which is set before dealing the actual damage and have it so that it does twice as much or just half as much damage depending on the type.
Here lies a bit of a complication. When it comes to a unit of the type, for example, Ground/Flying, it would have to be made so that the Pokemon of that type takes normal damage. This can be achieved with a simple, yet long, if/then/else statement. Basically, if the target unit of ability being cast has Ground ability and does not have Flying ability, it takes 0.5 X Dmg. If it has Flying ability and not Ground, it takes 2 X Dmg. And so on. I don't mind doing all the repetetive stuff, just gimme a copy of the map when you feel like taking a break and I'll plow right through a whole field of the triggers.
BTW, I am LOVING the idea of playing Single Player and then saving and being able to play online. It is soooo awesome! I would love to have that level of competition that you tend not to get from the Gameboy version. Anyway, hope to hear more soon on my further instructions. Good luck!