I too had this problem. I then found
this bug in the moodle bug
database, which describes the problem in depth.
Basically, to enable compatibility with most mail servers, it uses an old method of encoding 8bit characters to fit into a 7bit
SMTP stream. This has a 78 character limit, so = are inserted to split the message up. The image and links do not work because they also have characters replaced with = signs.
I managed to fix it on our mail
server by changing the $mail->encoding line in moodlelib from 'quoted-printable' to '8bit'. Other than this, you can change to plain text encoding (which we did while i investigated)
Maybe in a later version of moodle, this should be an option in the admin variables page to go alongside the SMTP options.