Colloquial language and slang overlap to a certain extent. Both are informal, and are more common in spoken than in written language. You might use either when speaking or writing to a friend; when speaking to a person in authority or writing to an acquaintance you might use colloquial language but avoid slang, and you would not use either in a formal letter or report.
The difference between them lies mainly in who uses them, and why. Colloquial language of informal everyday speech, and its words and phrases will be know and used naturally by most people having the language as their mother tongue.
Slang is more often used consciously in particular circumstances or within a restricted group. Each generation of teenagers makes up its own slang and uses it as a private language. Most trades and professions have their own slang words, often shorter and simpler words for technical terms, which are used partly for convenience and partly to show that the speaker is “in the trade” and “in the know“. Slang can be quite vivid and picturesque, and may be used in fun or to shock. It can also be used to show that the user is speaking informally; that he or she feels at ease or is trying to put the listener at ease.
Colloquial terms tend to stay in the language for a long time and to be fairly stable. Slang, on the other hand, may die or fairly quickly or may escape from restricted usage and be accepted into colloquial or standard English; clever, fun, and mob were all once regarded as slang. (This is less true of professional slang, where the ‘in’ group is stable although individual members of it come and go.)
Jargon refers to the language of a trade or profession, which may include the slang, used inappropriately. Technical language is perfectly all right when used between those who do not or cannot be expected to understand it, or when it seems to be used merely to impress rather than to communicate. Jargon can be used deliberately to gull the lay person, but is often the result of experts forgetting that their terminology needs explaining; computer instruction manuals are notorious examples.