I finally found out how to export emails from Entourage 2008 to MS Outlook 365. In case anyone else has this issue, here's the scoop:
1. Drag an email from Entourage 2008 to the desktop. It will have the .eml extension.
2. Control (or Right)-click the email, click Open With, and choose MS Outlook 365.
3. Outlook 365 will open and the email will be there.
You can also do a Get Info on that file, change Open With to Outlook, and then click Change All.
OS 10.14.3, iMac Retina 5K 27-inch, late 2014, 3.5 GHz Intel Core i5, 1 TB fusion drive, 16 GB RAM, Epson SureColor P600, Photoshop CC, Lightroom CC, MS Office 365