Eve Imo is one of the better mid game carys and one of my favorite assassin jungles. Most her power is related to kit mechanics and proper positioning.
The mechanics you need to get down are Q kiteing camps to reduce the damage you take early game. knowing how to use W and R with versatility, and hitting all targets with the enhanced E on your clears.
Common mistakes I see.
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Often times People only go for W charm. Plenty of times the slow is enough to get into range for ER. You can cast Q first at near max range, then get the W off on your target as the Q projectile is still traveling. this nets you the slow most the time, its also how you can successfully gank under pressure when you have not had time to position behind folks/cant get behind folks. Pretty much any time you want a kill but don't have the ability to get a full W charge this is the combo you should use. That said, if your not under pressure and have gotten good positioning you ABSOLUTLY want to charge W for the hard CC and MR shred.
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Folks don't use R for aggressive mobility. Examples here On rework release everybody was bitching about how eve had 0 mobility and I never understood that. her R is a Blink, Its good for kills, its good for excapes, and hey its also good for gap closing. In many situation they are really low hp, Its better to use R for a gap close then Flash. Its a lower CD and longer range mobility. Personally id rather have RQE on cd then Flash R on cd.
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Early game clears, when at risk of an invade, Take a bit more time on kite able camps like red and blue to evade damage with Q and W, keeping yourself healthy increases your ability to not die. When dealing with a risk of invade, don't throw W out the second a camp is in range, you should get vision out, save the W. Once you have vision then you can go for your camp (largest risks oftein being first clear 2nd buffs) If you have W up you have a better time smiteing your camp and then you can thank the enemy for the leash. If they sit in bush not starting a camp, you can wait for teammates, When this happens just wait. its a 0 gain situation but the enemy jungles taking a much higher risk. If they cant catch you starting the camp its in your favor for the first invade. you have hard CC, you can contest camp with smite and W, Your teammates can snag easy kill off a low level invader. Mid game your clearing fast enough and have perma stealth that invades become a pretty minor issue long as you keep vision up.
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People max E. The hell? don't. it only needs 1 point. Q is more damage per level up, and more importiant to your clear times, and thou you might not get all 3 mini casts off long as your hitting the first Q the debuff damage is easy to pop. W is good, hell some games your going to want to put extra points into it early for higher CC, Again use it for a slow as well as a charm, the duration on slow matters, 2 seconds of 65% is a good window to just walk up to some one and use the Empowered E.
Advantages of eve.
%damage burst. that E hits all champion classes hard mid game. Once its ramped up off your AP its nasty.
High single target hard CC. W can ruin peoples day.
Pretty much ward immune level 6 onwards. You know if they got a red or not when your near it, all other wards are a non issue,
unique stealth enables constant flanking in team fights, and aggressive scouting.
Passive puts Warmogs to shame.
Fast clears with some items.
Snowballs, power spikes pretty early on and keeps momentum for a good portion of the game.
Mid game carry, if you do well early your gonna have a lot of impact before any late game champions come on line, this gives a solo player the power to decide matches for their team.
Problems with eve,
Cant impact snowballed lanes early as well, need teammates to be smart and play from behind if they fked up in lane.
2+ lost lanes is a nightmare, you need to hit your spike, trying to save 2 lanes gone south is hard, if your not getting a kill your slapping a bandaid on a bleeding artery of a lane. They might be less screwed with you camping both lanes but your losing EXP and Gold so by the time your kit starts spiking your very behind in power, if ya don't have a good power base your unable to present a threat in teamfights to enemy carry's, your teams team fights crippled, and 3-4 players depending on lanes lost are low value.
Is a carry style champion and NEEDS some items to function well, its lower # of items compaired to others but getting deprived them hurts your viability.
Edit. If you like OP, I will record some ranked footage that might be useful for ya and can upload and post it here for ya. Note that my personal play style is to go HAM on the feast or famine.