1. nonstandard English - English usage which has not gained widespread literary, cultural or social acceptance
Nonstandard English refers to ungrammatical phrases and expressions that are not considered to be the 'standard' of the English language, or rather, grammatically correct and accepted. For example, expressions such as ain't, should of (instead of should have), double negatives, etc.
2. standard English - English usage which has gained literary, cultural, and social acceptance as appropriate for educated speakers
Standard English is what you learn in school - the way you are supposed to talk and write if you want to be considered an educated person. It is grammatically correct and represents the way literature and textbooks are written.
3. jargon - specialized vocabulary of a particular trade, sect, or profession
Jargon is the type of vocabulary that particular professions use, the words and expressions that aren't normally understood by people outside of that profession. For example, nominative predicate in linguistics, NPO in medicine, due diligence in law, etc.
4. informal English - variety of standard English used in casual and intimate conversations, letters, etc.
Informal English is something you normally use on an everyday basis, when talking to your friends and family, that is, when you are not in a formal situation.
5. general English - written or spoken variety of standard English used by most educated speakers
It is similar to standard English.
6. formal English - variety of standard written English used to express abstract or sophisticated ideas as are found in research papers or literary criticism
Formal English is also the type of English that you would use in formal situations - speaking to your professors, giving a presentation, writing a letter to your employer, etc. It is quite the opposite of informal English.
7. slang - colorful and eccentric language used by a particular social group; newly coined forms not yet accepted as informal idiom
Slang is usually used by young people and represents vocabulary created by them to describe various phenomena. For example, lit, swag, spill the tea, etc.
8. idiom - form of expression peculiar to a language or dialect and approved by usage
Idioms are combinations of random words that apart seem to not have any connection, but when brought together create a new meaning. For example, in hot water, which means to be in trouble.
9. gobbledygook - formal, pretentious, wordy, redundant writing which uses abstract or technical terms inappropriately
Usually, gobbledygook language doesn't make much sense or it is completely wrong. It is the type of language people use when they want to be smart, but end up making wrong connections between words. For example, there was an episode of Friends when Joey wanted to describe Chandler and Monica as 'warm, nice people with big hearts,' but he said 'They are humid prepossessing homo sapiens with full sized aortic pumps.'