From Bob Rozakis' Answer Man column in Flash #273 (1979):
Remember, this is 1979, so we're pre-Mongul, pre-Doomsday, pre-Anti-Monitor.
Much also hinges on how you're defining "strongest." The Composite Superman has all of the combined powers of the Legion Of Super-Heroes, so that's pretty powerful. And because, at least in the initial version, he had the combined strength and invulnerability of Supergirl, Mon-El and Ultra Boy, he was theoretically 3 times as strong as Superman.
As to the Parasite, it was a DC Science fact (at that time) that he couldn't ever absorb 100% of Superman's powers, because his cells couldn't handle it and he would inconveniently explode. So that would seem to leave him substantially behind the Composite Superman, who could be as powerful as 3 Supermen plus a whole heap of other powers. Plus, Parasite's power boosts were temporary.
Other candidates? Assuming you're excluding magic makers like Mxyzptlk, we could try Amazo--there have been a lot of inconsistencies in which powers he has over the years, but at the very least he has the combined powers of Wonder Woman, J'onn J'onzz, Aquaman, Flash and Green Lantern. So, depending on how you read it, he's near the Composite's level (plus, sometime he throws Superman's powers on there...).
You who else Rozakis ignored?
Darkseid.
That's not a huge surprise, though, as until the JSA/JLA/New Gods story in 1980, the New Gods post-Kirby had very little interaction with the rest of the DC Universe--Darkseid was mainly the "house villain" for the first attempted New Gods revival, not the universal threat he would later become. So at that point, he probably wasn't firmly established in everyone's mind as being that dang strong and powerful.
So, let's put it to you, peanut gallery--who was the "strongest villain" in DC circa 1979??