I think there's something behind the Neuroi, remember in the beginning when the three Hawkers flew into the maelstrom, and the sounds of the neuroi being attacked. I think the Neuroi are aliens but all the cores, and actual neuroi fighters are taken from the captured human pilots. The cores are probably the tortured souls of the young men who tried to fight the neuroi before the strikers were developed. The Neuroi are dicks.
Also now we know a few more powers
Mio: Ability to see long distances, and see the core of Neuroi (latent ability that can never be turned off)
Yoshika: Healing and shield
Yeager: Speed boost
Elia: Precognition (a few seconds at all times, or longer if using tarot cards)
Lynette: See long distances and predict the movements of her enemy (like seeing a few seconds into the future) (a combination of mio's and elia's powers, but at the cost of needing a lot of magical energy, which means it's hard to use while flying.)
Barkhorn: While they didn't sho anything, i think her power is related to the fact that she's the only strike witch who dual wields machine guns. Her power probably makes her much stronger than the others. allowing her to use two machine guns rather than just one.