Unusual, externally coy, cheap and nasty (6)
I believe the answer is:
shoddy
'cheap and nasty' is the definition.
(I've seen this before)
'unusual externally coy' is the wordplay.
'unusual' becomes 'odd' ('odd' can be similar in meaning to 'unusual').
'externally' means one lot of letters goes inside another.
'coy' becomes 'shy' (I've seen this before).
'odd' going within 'shy' is 'SHODDY'.
(Other definitions for shoddy that I've seen before include "Slapdash" , "Second-rate" , "Of inferior workmanship" , "Badly made or done" , "Cheap and poorly made" .)