First they're hi passed pretty extremely. Then it sounds like the reverb was bandpassed on a send channel. Decay ~2 seconds. I'm just listening through my laptop speakers, but it sounds like the track was also copied/recorded twice and hard panned l/r with even more of the lows/mids cut plus some harmonic excitement to give a little crispness on the edges. There's a dickton of subtle harmonies running throughout it to give it that Imogen Heap sound. I don't detect much delay, it sounds more like manual cutting to get the delay effects.

90% of it is just the performance though. The singer has one of those brittle, Ellie Goulding type voices that works well for this kind of stuff.

This has nothing to do with delay or reverb, but the vocal you are linking to have multiple layers of vocals - probably recorded like that. However, you can try out a plugin like http://www.waves.com/plugins/doubler for a similar effect.