Guess I'll take a stab at this first.
With King I don't think you should be losing the fireball war too badly, if at all. The reflector is well and good but King's light fireball doesn't travel full screen and is slow, so if you use that one and Athena reflects it, it will likely die out before it gets back to you. If you time it well you could probably rush in behind it and punish her with a tornado kick/jump in/whatever too. So be sure to mix up those two fireballs, or even jump Athena's fireball and then toss one out before you land while staying out of DP range. You can also use King's air fireball to alter her trajectory, so if Athena gets into a predictable rhythm on her fireball/DP trap keep that in mind.
If you're going to roll a fireball don't do it too close to her, just use the roll to get to a better position/avoid chip damage, which is pretty much the case with every light fireball in the game actually. If you roll it and land on top of her she can toss out a throw or command grab which will always catch regular rolls so don't use it when you'll land within range of a punish.
Her command grab (the thing where she tosses you up into the air) is invincible but it also has some pretty terrible recovery so if you can identify when the Athena player will use it and you jump, you'll get a full punish.
Her DP, like most of the cast, is pretty weak against cross ups since it lunges so far forward (especially good for Robert since his command cross up has some pretty great reach). It's great in the fireball/DP trap area, but if you are close enough to be able to cross her up, its pretty risky. Crystal bit (the glowing sparkle super) hits on both sides but is pretty risky to pull out on a whim unless the Athena player is constantly buffering the input or Athena's opponent is being predictable with their attacks.
Her normals tend to have pretty stubby reach or very specific uses/counters, except for j.CD, which is a pretty solid move. On the ground Her only far reaching moves are far s.D (slow), c.C/c.D (extremely punishable if hopped) and I guess s.A/s.B (both get beaten pretty handily by low profile moves like slides), so in poking range your characters should be pretty well off (Ralf and King I know have some far reaching normals, not sure on Robert). It is worth noting that at range Athena's far D can beat out low pokes and King's CD can be swept by Athena's crouch D as well so keep that in mind. If the reason you feel you're losing up close is solely due to her command grab or DP, you should assess what your habits are and figure out when you're getting hit with those moves since both are very punishable if Athena misses.
Hopefully some of the other Athena players will post their opinions, wouldn't mind having some thoughts on Athena vs King myself. My local King player gives me all kinds of trouble (not helped by the fact that he's also a straight up better player than me, but whatever).