In a repugnant manner (7)
(Other definitions for nastily that I've seen before include "Unpleasantly" , "Such is the threatening way" , "in a horrid way" , "In an unpleasant manner" .)
'in a repugnant manner' is the definition.
(I know this)
This is the entire clue.
(Other definitions for odiously that I've seen before include "in a repulsive way" , "In a repulsive manner" .)