Learn English – Difference between eloquent and articulate

[Edited, with examples:] There is some overlap between these terms. People will often even disagree whether a certain expression is best considered informal, or rather colloquial, etc. This is merely an attempt at cataloguing possible associations. If you have suggestions for improvement or refinement, do not hesitate.

Informal:

• This is the broadest, most neutral word. It just means that speech or writing is on the lower side of the formal–middle–informal spectrum. In informal situations, when your conduct is relaxed in all respects and etiquette matters less, you will use informal language accordingly.
• Varieties of language at lower or higher levels in the spectrum are often referred to as lower or higher registers, although the word register is not necessarily about high or low: it can also just be about varieties that are somehow different from the standard.
• Apart from that, it is neither negative nor positive; that's why it is the best term if you don't want to sound disapproving (and if colloquial is not an option).
• There are various degrees of (in)formality: it is usually not a yes–no distinction.
• Although perhaps higher-class people are sometimes expected to be in formal situations more often, and lower-class people are expected to care less about formality, there is no strict relation to perceived class. There are informal words or phrases that are frequently used by perceived 'higher classes' (loo), and, conversely, formal words that are not frequently used by same (Milady, toilet).

Colloquial:

Oxford English Dictionary: 2. spec. Of words, phrases, etc.: Belonging to common speech; characteristic of or proper to ordinary conversation, as distinguished from formal or elevated language. (The usual sense.)

• This is quite close to informal.
• It is mostly used with speech rather than writing, though not necessarily so.
• The word is also slightly stronger on average than informal (i.e. more informal).
• It suggests a yes–no qualification: saying more colloquial is not so common.
• It is usually neither positive nor negative, nor felt to be lower class.
• However, the euphemism "colloquial at best" is often used to mean that it is bad style, referring to a colloquialism used in the wrong setting.
• Because colloquial (and informal) language often varies locally or regionally, while formal language does so much less, it is sometimes associated with provincialisms or regionalisms. But I would consider this contingent, not essential to the term itself.

Slang:

• Slang can be a noun or an adjective; slangy means "resembling or constituting slang".
• It is more often negative than positive—but it can still easily be positive.
• In the formal–middle–informal spectrum, it is more informal than colloquial or informal.
• The word slang itself is a bit informal, while the other words on this page are not.

Oxford English Dictionary: 1. a. The special vocabulary used by any set of persons of a low or disreputable character; language of a low and vulgar type. [notice vulgar used ambiguously]

1. Originally, slang was language associated with low socio-economic class or character, and it is still used with that connotation, though by no means always.
2. A secondary sense has developed, that of general "group talk" in a mildly disapproving or mocking way—even if this group isn't lower class. This sense is now arguably more common than the first. It is often used ironically, as in lawyer slang.
3. A tertiary, entirely neutral sense, "any kind of non-standard group talk", is now commonly used in academia.

Vulgar:

• This means literally "of the people".The Oxford English Dictionary describes its development through the ages:

I. 3. Commonly or customarily used by the people of a country; ordinary, vernacular. In common use c 1525–1650; now arch.

II. 9. Belonging to the ordinary or common class in the community; not distinguished or marked off from this in any way; plebeian

II. 13. Having a common and offensively mean character; coarsely commonplace; lacking in refinement or good taste; uncultured, ill-bred.

• It can now be used to describe language in two ways:

1. The old-fashioned sense is as (II. 9.) above. It is still in use in dictionaries, but less frequent elsewhere.
2. The modern sense is close to (II. 13.), "obscene" or "filthy" to a greater or lesser degree; the lower classes were supposed to be liable to such language, and this sub-sense of (1.) came to dominate the word. So this is obviously even less formal than slang in its lower-class sense. In dictionaries, vulgar could be (1.) or (2.).

Other relevant words:

Jargon: technical or academic language or terminology. This is usually perceived to be somewhat formal, and inaccessible to those outside the field in question.

Vernacular: refers to the native language of normal people, when a different language is used by some groups in society. So this is about different languages, not merely different registers or levels of formality. Usually, the non-vernacular language is used by the educated or higher classes, such as Latin until ca. the 19th century.

I will give a few examples, best description first:

That ain't right.

• slang
• informal
• vulgar (1. of the common people), old-fashioned label
• perhaps colloquial

I will try and convince her.

• slightly informal
• colloquial
• some might call this slang or vulgar (1.), but it isn't felt to be connected with lower class by most people, nor with certain specific groups

That sucks.

• slang
• vulgar (2. obscene), old-fashioned label, because suck has lost its sexual connotation for many people
• vulgar (1. of the common people)
• informal (a bit too general)
• colloquial is possible, but not the best choice

If I was rich, I'd go to London.

• informal
• colloquial, but many people "would never say was", in neither speech nor writing
• slang or vulgar (1. of the common people): probably not

Usually, size connotes physical dimensions while magnitude connotes either a numerical measure (particularly a non-linear one) of any sort of amount or metaphorical size.

"What size is that screw?" (Physical dimensions)

"A problem of immense magnitude" (Metaphorical size)

You can also use size to mean metaphorical size, but you usually can't use magnitude alone to mean physical size. (Nobody would say "What's your sneaker magnitude?")