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I am wondering whether there is a commonly accepted rule about the word order of co-existing adverbs in a sentence.
For example, in the following sentences, 果然，昨天，直接，从学校 are adverbs. Which of the following 3 sentences is(are) correct? 1. 他果然昨天直接从学校去了图书馆 2. 他昨天果然从学校直接去了图书馆。 3. 他昨天果然直接从学校去了图书馆。
For a more complete discussion of adverbial order, see ＂实用现代汉语语法＂, page 524：
２。除了大部分副词以外，限制性的状语按下列顺序排列：
（１）表示时间的状语；
（２）表示语气以及在分句之间起关联作用的状语；
（３）表示目的、依据、关涉、协同的状语；
（４）表示处所、空间、方向、路线的状语；
（５）表示对象的状语。
果然 belongs to （２），thus it should come second after（１）time adverbial， more examples of（２）, adverbials （in fact adverbs） expressing mood （语气）：难道、岂、究竟、偏偏、索性、简直、大概、莫非、到底、原来
直接 may be counted among the majority of adverbs （大部分副词）not included above which should be immediately in front of the verb （or adjective predicate）。
For a more complete discussion see the quoted grammar.
Regarding the relative position of (1) and (2), according to Chinese: A Comprehensive Grammar p.148, adverbials indicating mood or tone are interchangeable in position with time expressions, thus confirming some of the comments above.
@S.Rhee What confuses me is that I don't see any rules in terms of the adverbials placement in a sentence. Not quite as you said "according to the general principle of modifier before modified head word it has to precede at least one other 状语", I know 他昨天直接果然从学校去了图书馆 isn't correct either.
从 A 去 (了) B, is the normal order. 直接从, and 直接去 is the same. 果然 and 昨天 should show as early as possible, even before 他.
A funny way is the following dialog:
A: "他昨天直接从学校去了女朋友家."
B: "果然!"
