Hello all,
Dostoievsky's style is not Nihilist. He displays Nihilism in many of his books (Notes from the underground, Karamazov Brothers, The Idiot, etc...) but he's not a nihilist himself as he deeply believes in god.
Dostoievsky is not an existentialist either as exitentialism relate to Sartre and co's style which is far from Dostoievsky's.
If I would define his style I would use words such as mystic, russian, deep-psychology, drama.