No, not like a vertebrate's nose.
They breathe, like all insects, through a row of holes down each side, connected to a web of tubes inside.
They can smell though. They smell with their antennae (feelers), again like all insects. Some insects can also "taste" with their feet -- not sure about crickets.
Grasshoppers have ears on their legs -- crickets may be the same, as they are in the same group of insects, and as they sing they must be able to hear too.