Unenchanted diamond sword, Smite 5 Knockback 2 Unbreaking 3 diamond sword, and Smite 4 Knockback 2 diamond sword all take 3 hits each to kill an unarmored zombie. Tested with a zombie spawner on many zombies. Smite damage does not seem to be applying.

Reproduced on Samsung S7 Edge running Android 6.0.1. With same device, reproduced on Gear VR edition.

Reproduced starting a new world on creative and spawning zombies. Takes 3 hits whether diamond sword unenchanted or smite 5. Notably, sharpness seems to work fine. Also, Smite seems to work fine on skeletons.