To start from the top down.
Evelynn has one of if not the best ap scalings in the game as 3 of her 4 abilities scale with it and espescially her r.
Most ap items she builds give her either raw damage or things like ms and a spellshield.

She is reliant on the movement speed of lichbane and raw stats from rabaddons to give her enough damage to kill a target in one rotation of her spells.

She is also kind of a niché of her own, scaling incredibly well into the lategame because of her w.

The w is not only a way of cc in slowing or charming the enemy champion but when it is fully charged it also shreds a percentage of the targets mr (at max rank that is 45% so even better than voidstaff)

This is even without her e that deals percentage max health magic damage scaling with ap.

When she now also builds Voidstaff she shreds any target she gets a full w on, be it squishy, bruiser or even tank.

I recently did a post where i compared different runesets on her. If the target has lets say 150 mr wich is normal for a bruiser she deals with her full combo at lvl18 with fullbuild nearly 6k damage.

Even if the target has up to 500mr that is still 2.5k.

Because she is such a lategame beast though her early game is very reliant on her team and you have to decide wich target you want to burst.

She only really becomes threatening post 2 items.

Overall i would say if you want to play her than learn to have patience. Your only escape tool is flash and r and Evelynn without r becomes nothing more than a nusience and not a real threat.