As Eddy:
As Katarina:
Your main strategy against Eddy is poking with d/f+1. He has a really hard time dealing with that move; he can't step it, and it tracks his auto sidestep punch that Eddy uses instead of step. It'll also float handstand very consistently, and can float RLX, but is not consistent in S2.
Probably the two most important things in this match-up are not giving him breathing room and knowing your punishes. 4,4,4/1,1/f,F+2,4 have limited utility in this match because of how often Eddy high crushes, but d/f+1 is much faster than most of what Eddy wants to throw at you. Once you teach him to respect it, you can play a more normal game against him, but you've got to keep it on the table to keep him honest. You can also backdash out of RLX mixups on HIT. :-P