sonderlich
particularly
Mostly used in negative or interrogative sentences and means 'especially' or 'to a high degree'. It softens a statement.
Das Wetter war heute nicht sonderlich gut.
The weather wasn't particularly good today.

particularly / peculiar
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particularly
Mostly used in negative or interrogative sentences and means 'especially' or 'to a high degree'. It softens a statement.
Das Wetter war heute nicht sonderlich gut.
The weather wasn't particularly good today.

'Sonderlich' (particularly/peculiar) is derived from 'Sonder-', which means 'separate' or 'special'. It is related to words like 'besonders' (especially/special) or 'absondern' (to separate), which explains the meaning 'special' or 'different from normal'.
Er hat seine eigenen, sonderlichen Ansichten zu diesem Thema.
He has his own peculiar views on this topic.
In the meaning 'particularly', 'sonderlich' is used almost exclusively in negative sentences. The combination 'nicht sonderlich' means 'not particularly' or 'not very'.
Ich war von dem Film nicht sonderlich begeistert.
I wasn't particularly enthusiastic about the film.
The meaning 'strange' or 'peculiar' is rather rare today and can sound old-fashioned or literary. It describes a person or their behavior as odd.
Der alte Mann im Nachbarhaus war ein sonderlicher Kauz.
The old man in the neighboring house was a peculiar character.
very
'sehr' and 'sonderlich' both have to do with the degree of a statement. 'sehr' intensifies directly: something is 'sehr gut' (very good), 'sehr teuer' (very expensive), or you are 'sehr' happy about something. 'sonderlich' is mostly used in negative or question sentences. 'Nicht sonderlich gut' means roughly 'not very good' or 'not particularly good'. So it often softens a statement. You normally do not say 'sonderlich gut' as a simple positive intensifier. For a clear, strong statement, use 'sehr'.

Milan findet den Film nicht sonderlich spannend.
Milan does not find the film particularly exciting.
Er ist sehr zufrieden, weil der Computer wieder funktioniert.
He is very satisfied because the computer is working again.