E.

I go for Paralellism and for conciseness.

Kuru, one of the strangest and most insidious diseases known, is no longer a major problem in New Guinea.

Thus by branching this compound sentence at "and", we can form two stand alone sentences. Hence Option E works, IMO.

Kuru, one of the strangest diseases known, is no longer a major problem in New Guinea.
+
Kuru, one of the most insidious diseases known, is no longer a major problem in New Guinea.

I initially picked E but switched to A because I felt that A maintains parallelism even though its not concise

one of the strangest

and

most insidious of the

Apparently I was wrong, because of the is not before the most insidious any more.

one of the strangest and most insidious itself is parallel as one of the applies to both strangest and most insidious.

Some times over analysis can hurt.

IMO : E

it is between choices A and E as per my understanding.
As in choice A - one of the strangest (what) and most insidious of ( what ) the deseases kown.
so we do not know that strangest modifies what
Hence E is better as it says kuru , one of the strangest and most insidious diseases

May be experts can pitch in to throw more light

"insidious" is an adjective and must be close to the noun it modifies. In this case it is "disease".

So it is E.