Inversion or fronting with "so"

These can be analysed either as instances of Subject-dependent inversion, or as Subject-postposing. One reason for choosing the latter is that postposing of the Subject is entirely optional. Notice that in the Original Poster's examples the two instances of so are quite different. They are both used as anaphoric pro-forms, but are being used to represent quite different types of phrase or clause which both have very different grammatical functions:

1. So says the preacher.

2. So began the fight.

In the first sentence so is the Complement of the verb say and represents a content clause. In (2) so is an Adjunct meaning something like in this way. When anaphoric so is preposed like this, we can also postpose the Subject. This is optional as can be seen from the examples below:

• So the preacher says.
• So the fight began.

(Notice that so must be stressed in the last example - probably to distinguish this usage from the usage of so as a connective or conjunction.)

The grammatical status of the proform so makes a big difference to the effect of postposing the Subject. When so is the pro-clause Complement of the verb say, the Subject postposing is quite normal. However, fronting of so used as a manner adjunct gives quite a literary effect: So endeth the lesson, So began my first term and so forth.

So is not a conjunction or conventional discourse connective in either of the Original Poster's sentences - although the word so can be used as a connective as is illustrated below:

• He took my ice-cream, so I punched him on the nose.

These are not examples of either fronting or inversion, although both of those grammatical structures are often explained using sentences starting with 'So...'. Typically, fronting with 'so' uses the word 'so' as an adverb. See http://random-idea-english.blogspot.co.uk/2014/09/exploring-inversion-and-fronting.html for examples.

In the examples given by the OP, 'so' acts a conjunction, rather than an adverb. "So began the fight" should be parsed as: "[because of the information given in previous sentences], the fight began". "So says the preacher" is equivalent to, "The preacher says [the information given in previous sentences]".

These sentence structures are unusual in modern spoken English, and are a bit formal or archaic sounding. I'd only use them if I was deliberately trying to use a 'Biblical' register. Examples of the same sentence form are "Thus Spoke Zarathustra.", or "And so all the rest of the human race will come to me, all the Gentiles whom I have called to be my own. So says The Lord..." [Acts 15:17].

In any case, they are just examples of starting a sentence with a conjunction, not inversion within a sentence.

SO at the beginning of a sentence is a summing up device(*So began the fight.) but equally an inducing agent preparing us for the narrative that follows(*So goes the rumour. There was a ...)meaning 'like this'.

As a parts of speech, SO is an adverb or coordinating conjunction. * I am so sorry. * He was ill, so he could not attend.

It means /like this /thus /in the manner /to the extent(relevant meanings only)

An adverb may be placed at the beginning of a sentence for modifying a whole sentence (anaphoric pro-form)or simply for emphasising. Take for example: * Down went the Titanic.

In the example of preacher, "so" means to me "like this" and that of fight,'thus'. SO is ADVERB in both the examples, nothing more.

Subject-verb inversion is not that common as is subject-auxiliary inversion. Still it is has evolved into a distinct pattern in which the verb should not necessarily be an auxiliary verb. Inversion is not limited to auxiliaries only. Cf.

*Beside the bed stood a lamp.

Admittedly rupture of the canonical order takes place mostly in holy books, Ecclesiastical writings, short stories or literal pieces.

It is said that introductory adverbs or adverbials are used with 'be'/linking verbs (*So be it) and verb of direction ((*So can Tercy). 'So' in the sense 'thus'/'like this'can be used with almost all the verbs in inversion. Of course, necessity primarily dictates discretion.