Not only did the systematic clearing of forests in the United States

Of the four examples you gave, only the first would be acceptable.

The second is wrong because the parallelism is off -- two parallel verbs should be interchangeable. But you clearly can't write, "Not did he harassed..."

The third and fourth examples contain a phrase ("not only he stole") that doesn't make sense. I could write, "He not only stole," in which case he performed some second action. But "not only he stole" is incorrect, partly because it isn't clear if someone else is also stealing or if "he" is doing something else.

Be careful about trying to create a rule here. It's true that if I wrote, "Not only did Tim x and y..." you'd expect the "did" to be applied to both x and y, but that's more a function of how parallelism works than about any rule regarding the usage of "did."

I hope that clears things up!

Not only did the systematic clearing of forests in the United States create farmland (especially in the Northeast) and gave consumers relatively inexpensive houses and furniture, but it also caused erosion and very quickly deforested whole regions.

Option Elimination -

(A) Not only did the systematic clearing of forests in the United States create farmland (especially in the Northeast) and gave consumers relatively inexpensive houses and furniture, but it also - the primary issue here is "did create" and "did gave." It has to be "give." Moreover, the construction of not only X but also Y places equal emphasis on both X and Y, while the construction of X but Y presents a contrast (It indicates that X is true or applicable, but Y presents an opposing or limiting factor.)

(B) Not only did the systematic clearing of forests in the United States create farmland (especially in the Northeast), which gave consumers relatively inexpensive houses and furniture, but also - "which" referring to "farmland" is not correct. Moreover, there is no subject after but. We need "it."

(C) The systematic clearing of forests in the United States, creating farmland (especially in the Northeast) and giving consumers relatively inexpensive houses and furniture, but also - No verb before "but."

(D) The systematic clearing of forests in the United States created farmland (especially in the Northeast) and gave consumers relatively inexpensive houses and furniture, but it also - ok. We don't need "not only" before "but also." "but also," here is a deception (mainly "also") because if we over-rely on the rules, then we'll keep searching "not only," and there is a high probability we cross it off. This is a simple X but Y construction wherein X showcases the positives and Y as the negative factors.

(E) The systematic clearing of forests in the United States not only created farmland (especially in the Northeast), giving consumers relatively inexpensive houses and furniture, but it - Now the subject is outside of the "not only," so it is applicable for both. But a repetition hereafter "but" is not required. It was required in A because the subject was hidden in the inverted structure after "not only," but here, it is clear and outside of "not only."