First thing you want to try is to upgrade elog to the last version. Older versions have problems in including images.
Then you want to check the "Email Format" in your elogd.cfg configuration file. Only if "16" is included there, then attachments are sent as email attachments and images will be included in yoru email. If not, only a link of the image is included in your email, and you correctly realized that you then cannot view the image because your email client does not knwo how to authenticate itself at the elog server.
When I use the email notification for an entry with images in the text, it seems the email server cannot retrieve the image. When I inspected the URL of the image it went to the login page.
Is that because the logbook has a password config that the access from the URL of the image needs authentication? Or I am just using the image upload the wrong way .