It is a relatively straightforward question, and Ahmad's is the correct answer, except that "outburst" is a countable noun and we need to put the article "an" there. So the correct answer is "There was no reason whatever for such an outburst." Other variations do not make sense, considering the context.

The correct order should be : There was no reason whatever for such outburst .

(For whatever reason there was no) such outburst. Could correctly be stated as such: For whatever reason, there was no such outburst. Since you are starting the sentence with a prepositional phrase, you must place a comma between it and the subject. The subject in this sentence is "there", the verb is "was", and the direct object is "outburst", which is modified by "such", and "such" is modified by "no". You could also rephrase this sentence: There was no such outburst for whatever reason. For whatever reason is a prepositional phrase, to be more exact an adverb phrase. An adverb phrase answers the question: Who? What? Where? When? Why? or To what extent? Since it answers WHY? (for whatever reason) and it modifies the verb WAS, it can also be written: There was, for whatever reason, no such outburst.

The second sentence makes sense to me.

Thank you for all answers.