According to multiple Wikipedia articles (1 2 3 4 5 6), "Elektra" was the name of the layout engine in Opera 4-6. This is also widely believed to be the case across the Web, as a quick Google search reveals.
However, all of these pages, including Wikipedia, are incorrect.
"Elektra" was actually the codename of the Opera 4 browser, just like Kestrel was the codename for Opera 9.5 and Peregrine is the codename for Opera 10. I don't think the engine had an actual name until it was rewritten for Opera 7. Today, it is known as Presto.
Elektra is actually mentioned in a press release from 1999:
The new Windows version, Opera 4.0 Elektra, is scheduled to be released at the end of this year.
As Rijk also pointed out a while back, Elektra was a complete browser, and designed to make it easier to port Opera to new platforms.
As a sidenote, our group of volunteers under NDA is called "The Elektrans". The group was established in connection with the Opera 4 release, and started out as a Windows group. Today, there are several different volunteer groups under NDA for different platforms and focus areas.