This answer is going to be long, and will have multiple parts, because there’s some background I need to explain first.
Built-in parameters
FMOD Studio has three different built-in parameters that describe the relative facings of the listener and emitter: Direction, Event Cone Angle, and Event Orientation. While these three parameters are related, they each describe something very different.
Direction (big D) is the angle between the direction (small d) the listener is facing in and the direction (small d again) from it to the emitter. Negative values represent the emitter being to the listener’s left, and positive values to the listener’s right. Thus, if the emitter is directly in front of the listener, Direction is 0 degrees; if the emitter directly to the listener’s left, Direction is -90 degrees; if the emitter directly to the listener’s right, Direction is 90 degrees; and if the emitter is directly behind the listener, Direction is 180 degrees (or -180 degrees, if you prefer).
Direction is sometimes used to make events that get louder when the listener focuses on them, or which make strange noises whenever the listener looks away.
Event Cone Angle is almost the reverse of Direction: It’s the angle between the direction (small d) the emitter is facing in and the direction (small d again) from it to the listener. Unlike the Direction, Event Cone Angle does not distinguish between left and right. Thus, if the listener is directly in front of the emitter, Event Cone Angle is 0 degrees; if the listener is directly to the emitter’s left, Event Cone Angle is 90 degrees; if the listener is directly to the listener’s right, Event Cone Angle is 90 degrees; and if the listener is directly behind the emitter, Event Cone Angle is 180 degrees.
Event Cone Angle is commonly used to to make events that sound loudest when you’re in front of them, and quieter from other angles. (The name ‘event one angle’ is a holdover from FMOD Designer, in which Event Cone Angle could only be used to attenuate volume in a conical pattern.)
Event Orientation is the angle between the direction (small d) the listener is facing in and the direction (small d) the emitter is facing in. Thus, if the emitter and listener are facing the same way, Event Orientation is 0 degrees; if the emitter is facing to the east while the listener is facing north, Event Orientation is 90 degrees; if the emitter is facing to the east while the listener is facing south, Event Orientation is -90 degrees, and if the emitter is facing south-west while the listener is facing north-east, Event Orientation is 180 degrees (or -180 degrees, if you prefer).
Event Orientation is almost never needed, but is occasionally used to create in-game compasses with audible properties.
You can observe the behavior of all these parameters by using the 3D Preview: You can click and drag the arrow icon to reposition the emitter, you can rotate the emitter by spinning the mouse wheel, and the listener is always in the center of the circle, facing forward (up).
The 3D Panner Effect
The 3D Panner is an effect that applies panning to an event’s master track based on the event’s position in 3D space relative to the listener. It both attenuates the event based on distance, and pans the event based on its Direction (big D).
Your Situation
You want an event that is panned based on which side of the listener it is on, and you also want it to sound different based on which side of it the listener stands. You therefore want both a 3D Panner effect, and for the sound modules in the event to be automated based on Event Cone Angle. There is absolutely nothing preventing both of these things from existing in the same event.
There is one wrinkle. As I mentioned above, Event Cone Angle does not distinguish between left and right. This means that while it’s possible to use it to make an event that sounds different when you’re in front of it compared to being beside it or behind it, it’s not possible to make an event that sounds different when you’re standing on its right side as opposed to standing on its left. If you want to make an event with bilateral asymmetry, you need to work around this limitation by creating an event that represents the left/right asymmetry as front/back asymmetry, and position it in the same location as the original event, but perpendicular to it.
Incidentally, you mentioned in a comment that Event Cone Angle would for some reason require you to make four separate events. This is incorrect; It would have been true if you were using FMOD Designer, but only because FMOD Designer’s version of Event Cone Angle was not as flexible as the one in FMOD Studio, and did not allow arbitrary automation of volume.