What does it mean that we are "like gods, knowing good and evil"?
The phrase is a self-defining construct. It says that to be a divine being, like a god, is the same as to know the categories "good" and "evil". And this is true of us.
I think it would be wrong to expand this clause so as to say that we know whether a person or thing is a good person or an evil thing. The evidence, I think, shows that we humans are not particularly adept at making assignments into these categories.
But we do know the categories themselves; we are familiar with the terms and we have some grasp of the power of the concept. Indeed, we overuse the categories "good" and "evil". Often we declare something to be good when all we really mean is that it is efficacious. Or we categorize as evil everyone who thwarts our quest for some transient benefit.
God -- the real one, the one who is not merely "like" a god -- we understand to be not only the true arbiter between good and evil but even the definition of good: God alone is good. Those who are with God and supporting the purposes of God are classifiable as good. Those who oppose God are classifiable as evil. (You see why we are not so adept at classification. We do not really understand God very well.)
My cat and dog, wonderful as they are, show no sign of grasping the categories "good" and "evil". They understand "warm" and "powerful" and "edible" (although the dog is overly expansive in his interpretation of "edible"). The cat and dog are sometimes surprisingly like humans, but they not like gods.
Humans are sometimes like cats and dogs; sometimes too much so. But we are also "like gods" because we know "good" and "evil".