I play Evil Ryu but I'll be honest, I don't play him the way he's suppose to be played. Part of that is because of my own play style preference, and the other part is my execution and reactions is just not good enough. At a basic level, Evil Ryu plays almost exactly like Ryu, you zone with fireballs and play footsies. He's not a vortex character or rush down character. People make that assumption because of his damage and low health.
The key to Evil Ryu's damage is to build meter to FADC into his axe kick combo. The most common way to land this is from FADC'ing his low forward into LK axe kick or fireball. You have to have really good reactions though because with low forward fireball, you pretty much have only one move to confirm because you have to FADC fireball almost immediately. From here you also have to know if you're in range for his cl. or cr. HP. If not you'll have to use one of his farther reaching normals to extend the combo. With LK axe kick it's a much easier confirm, but it's unsafe on block so you can get punished for it. Even on hit you're only +3 so you're forced to land a 1f link to extend the combo.
If you have the execution and reactions, that's Evil Ryu's main game plan in a nut shell. I don't do this because I can't land it consistently and I've practiced for a long time now. I personally play pretty aggressive and gimmicky. I go for resets and mix ups that aren't considered "good", but I do it anyways because that's the way I like to play. Regardless of your style, he's still a shoto and has the shoto basics. So you can always rely on that. Zone with fireballs, anti-air jump ins with DP, have a strong footsie game, etc.
If you got any other questions about Evil Ryu, I'll try my best to answer.