The same rodents overwhelming Illinois home (8)
I believe the answer is:
domicile
'home' is the definition.
(synonyms)
'the same rodents overwhelming illinois' is the wordplay.
'the same' becomes 'do' (abbreviation for ditto).
'rodents' becomes 'mice' (mouse is a kind of rodent).
'overwhelming' is an insertion indicator.
'illinois' becomes 'IL' (abbreviation).
'mice' placed around 'il' is 'micile'.
'do'+'micile'='DOMICILE'
(Other definitions for domicile that I've seen before include "Legal place of residence" , "A person's place of residence" , "Dwelling" , "Place of residence, abode" , "One's permanent residence" .)