Language
Language refers to the category of words an author uses. It is closely tied to diction.
Slang
I assume you are all familiar with the slang of previous generations: “cool,” “gnarly,” “far out,” etc. (For this, [i.e. your] generation, I use UrbanDictionary.com[1].) So, slang is used in everyday conversation, but never in academic or professional writing.
Colloquialism
Colloquialisms are similar. Droppin’ the “g” after words ending in “-ing” is a Southern colloquialism. These words are usually defined by a geographical location (a good dictionary will tell you the location in which these words are used), but as you can see, slang and colloquialisms are very similar. The second word is just longer.
Jargon
Jargon, however, is quite different from the other two. Jargon is a word for any set of words devoted to a particular task usually used by a particular group or organization. It is used amongst people that are familiar with the topic being discussed. For example, there can be sailing jargon (”aft,” “starboard,” “boom,” etc.), as well as sailing slang and colloquialisms (”avast matey,” “shiver me timbers”). For English students, “gerund,” “apostrophe,” “synecdoche,” and “metonymy” are jargon words. Those who have never studied the language would not understand the technical terms. I am sure you can come up with a few for computer programming, gaming, sports, auto repair, astrophysics, or any other hobby or study.
When an author uses jargon (without defining it), he or she is speaking to a specific audience. So, if you find your author using several words that you are unfamiliar with, grab a dictionary and look them up. If, for example, you look up “humor” in the Merriam-Webster dictionary, you will find “hu·mor noun . . . 2 a in medieval physiology” below the standard definitions. “In medieval physiology” applies to the word when it is used as jargon.
Use
Language can make a speaker seem closer to his or her audience (think ethos), but may also cause the speaker to seem like an “outsider,” so pay close attention to the speaker/writer’s language if it seems foreign or specific to one group.