What do you mean when you say that your domains are either Gmail or Outlook? As far as I know, many EDU domains have access to both Microsoft's and Google's education benefits which might include the unlimited Google Drive and the 1 TB of OneDrive (and possibly Office 365).
No, if it is Gmail in order to use Office 365 you need to make Office account which includes Outlook email. I am not sure if you can get 1TB OneDrive if your email is from Gmail. Please check it yourself
here.
On the other hand, if you start with Outlook, you
cannot make Gmail account. FYI, if your email is Gmail, you automatically get unlimited storage of Google Drive.
Do you also know if any of them have access to DreamSpark? If any of them do, I would certainly be interested. My current university account has full access to it.
I never tried DreamSpark.