With this, I can clear out the lingering smell of breakfast and clean the air.
Literal
This [with-で] morning-meal [gen-の] lingering-scent [things-like-など] [obj-を] sweep-away-[and-て] air [obj-を] clean make-able.
残り香 'lingering scent' is a compound of 残り 'remaining' + 香 'fragrance/scent.' 一掃する 'to sweep away completely' is a formal compound verb (一 'one/complete' + 掃 'sweep'). きれいにできる uses the pattern [na-adj]にする 'make it X' in its potential form — 'can make clean.'