What is the definition of language style?
Language style is the way of speaking/writing depending on circumstances of doing that, person (or people) to whom you are speaking or writing.
There are many language styles. Examples can be seen in letters' beginings or endings.
In officicial style you would use forms like:
Dear Sir/Madam or Dear Mr. X for beginning and Yours faithfully or Your cincerely for endings.
In unofficial or coloquial style you can begin your letters with Hi or Dear X and end them with Love or things like that.
These are only two basic examples of language style used mainly in writing. There can be even more language styles in speaking. They can be seen in the grammar structures, vocabiulary, tone, etc.
They depend on speakers' education, economical situation, current events in life (a person speaks differently when he/she has just got a better job, and differently when he/she has just lost someone)