K athena is very good, my main team consists of an r1 K athena, always.
JD gives her free jump-in, because her jumping roundhouse has great range (great angle too, perfect for using after a JDed anti-air).
for anti air usually st.MP is enough for most situations, if not you can always JD stuff. ppl always say st.MK is great anti crossups etc. but i never really tried it; never really had the need to. crouching fierce is a great anti air too against some air attacks, but not all. i havent really figured out what type of air attacks beat it, i think its the ones with less vertical priority/hit frame. (non-crossups)
i don’t recommend throwing a lotta fireballs with athena unless your opponent goes into defense mode or just turtles. her fireball has slow startup and recovery.
straight jump up roundhouse is almost blanka-slap-level-good. same usage as that.
i agree with jaehoon that jumping forward isnt that good. i dont really use it at all. i find jumping roundhouse and butt bounce to be enough for air attacks. butt bounce has godly priority, though not invincible (so loses to shoryukens).
i dont use her sweep at all, her cr.fierce is too good a substitution for sweep. you can probably score 2 cr.fierces in a row if an opponent isnt too familiar with fighting against athena 
her teleport comes in handy at certain situations. some situations where i would use it is, when running away from a flashing lv 3 S/N/K groover, get to the corner, when he comes your way, HK teleport outta there. if you know your positions well, you can always teleport -> command grab. but it’s easy to get thrown out of it as teleport recovers slow and command grab starts slow too.
[edit]
oh, and K athena DOES have an answer for RC blanka balls and the like, that might be something to consider for using her in K groove. JD the blanka ball, run in crouching fierce. works every time. i would think P groove would work too for the same reason, so depends on how good are you at parrying, personally i think JDing is THAT much easier than parrying. maybe im just used to it.