Feeling like this bully, oddly overlooked (4)
I believe the answer is:
soul
'feeling' is the definition.
(soul is a kind of feeling)
'like this bully oddly overlooked' is the wordplay.
'like this' becomes 'so'.
'oddly overlooked' means one should take alternating letters.
The alternate letters of 'bully' are 'ul'.
'so'+'ul'='SOUL'
(Other definitions for soul that I've seen before include "The immaterial part of a person" , "Music genre; human spirit" , "Glaser's partner" , "Deep feeling - music genre" , "Essence" .)