Thanks for your reply. The problem wasn't in the pasting -- the links looked fine when I pasted them. The problem occurred when I hit "Send" -- as the email was sending,it would flicker a bit, and the link would change from what I had pasted (starting with "http://www.evernote.com") into one of the long weird things beginning with "https://www.bixel1.net".
I'm using Evernote v126.96.36.19927 (no updates are available) and Outlook 2016.
Having said all that, the problem appears to have fixed itself after lasting two days. This morning when I logged in, it was working fine. Go figure.