Dear NT:
>
> You wrote:
> Which are correct (they are supposed to mean the same):
> 1-Nowadays many houses are constructed as in the sixties.
> 2-Nowadays many houses are constructed like in the sixties.
> 3-Nowadays many houses are constructed like they were in the sixties.
> 4-Nowadays many houses are constructed like houses were decorated in the
> sixties.
>
> What does the “they” in sentence 3 stand for?
>
The clearest and the most likely to be heard is #3. Technically, in formal English you should say “as” rather than “like,” but in informal and everyday speech that rule is often disregarded.

#1 and #2 would be OK in context perhaps but are a little ambiguous. #4 means something else since “construction” and “decoration” have two different meanings.

There is only one plural noun in the sentence, so it is safe to assume that “they” refers to “houses.” This is especially clear because of the parallel formation of the two clauses (subject + verb to be).