How long is your migration to Office 365 going to take?

 Your rate limiting step in a migration is moving and synchronizing your email.

It's going to take weeks at a minimum if you have a site of any size.  More likely it will take months.

Why?  Because likely you have over 100 Gb of email files and that's just going to take a while to process and (thanks to the IMAP protocol) continuously synchronize until your cut-over date.

The IMAP protocol is a godsend for these purposes.  So getting started early and watching the amount of data you have and have moved is going to be a key part of the process. 

Sadly, no ready protocol exists for calendars, contacts, and tasks.  So you need to one-off those and you should expect them to take hours just before cut-over.

That's why testing the snot out of everything is our mantra.