Hi there!
The JR East pass is only valid within this area which unfortunately does not include Nagoya, the JR Pass however would cover this journey.
Since you say Osaka Airport, do you mean Kansai Airport or Itami? Travel from Kansai Airport is covered while Itami is best reached by bus (and thus not). Travel from Shin-Osaka to Tokyo and Narita Airport is also included.
As for travel times
Nagano -> Tokyo is 83 Minutes
Nagano -> Nagoya 106 Minutes
Nagano -> Osaka 267 Minutes
You can use Hyperdia to check for route information, it includes travel time, ticket fares and lots more!
-Daniel