Quiet and strange — that is street most badly built? (9)

'most badly built?' is the definition.
(shoddy can mean badly built)

'quiet and strange that is street' is the wordplay.
'quiet' becomes 'sh' (both can be said to tell someone to be quiet).
'and' means one lot of letters go next to another.
'strange' becomes 'odd' (I've seen this before).
'that is' becomes 'ie' (short for Latin 'id est', 'that is').
'street' becomes 'st' (abbreviation).
'sh'+'odd'+'ie'+'st'='SHODDIEST'