The correct option is C It was raining and thundering incessantly while I was sleeping.
An adverb clause can be used to combine two sentences into one complex sentence; where the adverb clause becomes a subordinate clause. Depending on the relation between the two, the adverb is used.
The given sentences share a relation of time, where two events occur at the same time. Option C contains an adverb clause "while I was sleeping" which expresses time, hence C is correct.
Option A does not contain an adverb clause; 'always' does not form a suitable adverb clause in relation to the sentences. Hence A is incorrect.
Option B contains an Illative compound conjunction that expresses an inference between two clauses, neither is the sentence complex nor does it refer to inference, hence B is incorrect.
Option D contains an adverb clause of reason 'because...' whereas the relation between the sentences is time. Hence option D is incorrect.