I would recommend using the preposition "in", thereby treating it grammatically as the noun "media". Compound nouns tend to disregard the functionalities of the noun which has been added to the original one. One would always say "in" the media" and not "on" the media. Examples of word use in, for instance, Oxford, support this rule:
‘85 % of women made decisions based on information they read in social media.’ (https://en.oxforddictionaries.com/definition/social_media)
Using Facebook and Twitter as exact synonyms for the term "social media" is misleading as they are merely examples of social media sites. When it comes to functional grammar, one should be careful interpreting contents over function.
Lastly, since social media is an abstract concept (similar to 'nature', 'society' etc.), one should avoid using the definite article "the" at all times, as it narrows down the meaning of the term.
My suggestion would be to write "on various social media sites" or "in various social media" if one desires to express volume. Again, please note that the preposition changes to match the post-head string of the prepositional phrase, which is "sites" in the first example and "media" in the latter.