There are 4 types of abbreviations I know for "versus":
I generally use the last one in the list, but I want to stick to one and use only that one. Which one is more proper (or more prevalent), and why?
Extra question: Which one should be preferred in scientific papers?
In legal contexts, the abbreviation "v." is used. Elsewhere, the most common is "vs.". In formal contexts (e.g. scientific papers), it is probably best to have the period at the end of the abbreviation. I assume you would be using this abbreviation in graphs/charts/titles and things like that; the abbreviation would be appropriate in these places, but not within normal prose of the paper.
v. is primarily used in legal contexts. In a scientific article, you would generally use vs..
vs. is preferred over v. in most common contexts - not that it is necessarily used frequently itself. Here are some examples of vs. being used in scholarly articles: scholar.google.com/scholar?q=%22vs%22. There are some false matches, but I am having trouble finding a more accurate set of articles.
Preamble
As well as considering the four alternatives listed in the question, I shall also discuss the tendency to italicize them (being of Latin origin), especially when ‘v’ is used. Thus, there are eight alternatives. The choice you make depends to some extent on the context (legal v. sport) and whether you are writing American or British English. This is mentioned in a related question on this list regarding ‘versus’.
vs and vs.
Despite the fact that the Oxford English Dictionary online ignores it, vs. is is not only used, but appears to be more common than vs without the point, as shown by cursory browsing (e.g. example below) and this Google Books ngram:
However, I must admit I am not sure where this is being used as it is not used in either a legal or sporting context (see below). Someone mentioned a scientific context, but as a professional scientist I can’t ever recall using it
Legal use
Both in the US and Great Britain, the traditional legal abbreviation is ‘v.’. The original tendency to initialize it is illustrated with two facimilies:
[(a) Brown v. Board of Education, 1953; (b) Travers v. Wilde and Wilde, 1864 — Because of the use of italics for the title of the court case, the setting of ‘v.’ in Roman indicates its italic original.]
Contemporary usage is unitalicized ‘v.’, although there is a new tendency to use ‘vs.’ in the US press. This is exemplified by an article in the New York Daily News of May 16th, 2015, in which the headline is “Brown vs. Board of Ed. decision…” but the (modern) caption to an original 1954 photo on the same page is “Brown v. Board of Education segregation coverage” (my emboldening).
Sporting Fixtures
As far as I can ascertain the use of ‘v.’ or ‘v’ in sporting fixtures is a British phenomenon, not found in the US. I have used the ‘England versus Australia’ cricket fixture to follow the historical usage. A Google ngram shows that for many years ‘v.’ was almost the sole usage, but from the mid-1970s the use of ‘v’ has grown, so that today it is equally common, and is certainly what will be found on websites (e.g. BBC Sport). There was low usage of ‘vs.’, but ‘vs’ was not found.
Whitaker’s Almanack for 1946 shows italicization: ‘v.’, although Hazell’s Annual for 1913 does not:
I always use "vs." (I don't know if this is very useful jeje) but I quote here an answer from Yahoo Answers that might help.
Spell out the word versus unless you're reporting game scores, when you would use vs.; when you're citing legal documents, use the abbreviation v. (with the period)
v/sv.(with a dot) butvs(no dot). Likewise,Mrwithout a dot. I always thought this was a well established rule and am surprised no-one mentioned it.