Why the other options are wrong?

If you look at the sentence, you can start to analyze it by crossing out all of its parenthetical and nonrestrictive components:

The orthodox view of a single intelligence, widely, if wrongly, accepted today in the minds of the general population, --------------, who by the second decade of this century had put forth its major precepts.

In short, we are left with this:

The orthodox view of a single intelligence --------------.

We can now consider the following four trimmed-down versions of the sentence:

1. ✘ The orthodox view of a single intelligence a few researchers whose energies and convictions originated those.
2. ✔ The orthodox view of a single intelligence originated from the energies and convictions of a few researchers.
3. ✘ The orthodox view of a single intelligence the energies and convictions of which originated and a few researchers.
4. ？ The orthodox view of a single intelligence with which originated the energies and convictions of a few researchers.

The second sentence has a clear subject and verb.

The fourth sentence doesn't work as it stands, but it might if a verb were to follow what's there.

(The first and third sentences can't be corrected by the simple addition of anything after what exists.)

For instance, the fourth sentence would work (at least syntactically) if was wrong were added to it:

The orthodox view ^{[of a single intelligence with which originated the energies and convictions of a few researchers]}was wrong.

Here, the subject—which is actually everything up to was wrong (I used square brackets to show the simplified subject)—is followed by a verb.

But the original sentence doesn't use that wording. When the final piece of the original sentence is added back, the second sentence remains grammatical, but the fourth sentence stays ungrammatical:

2. ✔ The orthodox view of a single intelligence originated from the energies and convictions of a few researchers, who by the second decade of this century had put forth its major precepts.

4. ✘ The orthodox view ^{[of a single intelligence with which originated the energies and convictions of a few researchers, who by the second decade of this century had put forth its major precepts].}

By the process of elimination, all of the sentences are ungrammatical with the exception of the second sentence.