LICE AUGH!!!! HOW WHY NOOOOOOOOO!!?

ok my lil sisters have acquired lice from our new horse that we saved whats sad is your not supposed to catch it so why do my sisters have the exact same bug as the horse there small brown skinny bugs im needing a few things 1. i need a link with the pix of different lice and there exact name then 2. i need a link that will direct me to a way of disposing of the lice 3. i need to know if my dumb *** step father puting oil on it is going to hurt the horse this horse is a miny pony so idk but plz help thank you