格外 + [adjective]
格外 + [verb]
格外 says something is more so than it normally is, and the sentence usually gives the reason: after rain, at a festival, on a first time. It's neutral to written, and common in descriptive writing.
It also goes before verbs of feeling or care.
格外 compares a thing with its own usual state. 尤其 and 特别是 pick one item out of a group. So 格外 can't introduce an example.
格外 already says the degree, so 很 and 非常 don't go with it.