What is the distinction between notion and idea

Question

This is my first post ever. I am currently working hard on expending my English vocabulary as well as my spelling abilities.

There is a word that is causing me trouble at this time. The word is notion.

I would like to know what is the distinction between the following words:

• notion,
• idea,
• belief,
• and conception

Some people say notion means a loose concept or a loose idea. I mainly use the Oxford dictionary.Here are some definitions and examples from the oxford dictionary of English.

Origin: Late Middle English: from Latin notio(n-) 'idea', from notus 'known', past participle of noscere.

There are 3 definition for notion;nevertheless, I am concerned with merely one of them.

def1: (noun) conception of or belief about something: children have different notions about the roles of their parents. I had no notion of what her words meant.

for the above example, I feel that I could say: 

I had no idea of what her words meant.

The meaning would be the same, right?

example 1: Though the concept of beauty is timeless, notions of what constitutes the perfect physical form have changed over time.

I feel that I don't understand the use of "notion" in this sentence.

example 2: There are different notions of what public opinion is.

 This could be replaced with 'idea' or 'belief' or 'conception' right ?

example 3: Chinese people seem to have more affection for, and put more belief in, Western notions and practices.

 This looks like an example I would use. 
 I feel that I would have replaced notions with concepts or ideas.

Here are definition of the other words I am comparing notions to.

http://www.oxforddictionaries.com/definition/english/idea

http://www.oxforddictionaries.com/definition/english/belief

Merriam Webster definition for conception is "an idea or opinion"

full definition:

• an individual's conception or impression of something known, experienced, or imagined
• an inclusive general concept
• a theory or belief held by a person or group

So opinion and impression is part of the merriam webster's definition.

The contexts in which I will use this word, I think is for everyday talk. I do work a customer service job where I troubleshoot mobile phones. I do want to write sociology and philosophy papers.

Answer 1

Synonym Discussion of IDEA
(a direct quote from Merriam-Webster dictionary)

Idea, concept, conception, thought, notion, and impression mean what exists in the mind as a representation (as of something comprehended) or as a formulation (as of a plan).

Idea may apply to a mental image or formulation of something seen or known or imagined, to a pure abstraction, or to something assumed or vaguely sensed: "innovative ideas", "my idea of paradise"

Concept may apply to the idea formed by consideration of instances of a species or genus or, more broadly, to any idea of what a thing ought to be:
"a society with no concept of private property"

Conception is often interchangeable with concept; it may stress the process of imagining or formulating rather than the result:
"our changing conception of what constitutes art"

Thought is likely to suggest the result of reflecting, reasoning, or meditating rather than of imagining:
"commit your thoughts to paper"

Notion suggests an idea not much resolved by analysis or reflection and may suggest the capricious or accidental:
"you have the oddest notions"

Impression applies to an idea or notion resulting immediately from some stimulation of the senses:
"the first impression is of soaring height"

Answer 2

As generally used in the US, "notion" (in the non-sewing sense) means an idea which, while perhaps not fully formed, tends to "nag" the holder of it, insinuating it's presence into thoughts without being intentionally "called up".

If I have a notion to write a book, eg, the idea would be sitting there in the back of my mind and would make it's presence known at odd times when I was thinking about something else.

As such, a notion has a more powerful sway on the individual than does a regular thought or idea, even though it may not be (and in fact often isn't) all that well-formed and well-conceived. It can, I suppose, be a borderline compulsion. (I suspect that psychology has a term for this.)

(It should be said that the word is also used in a less specific fashion to simply mean an "inclination". "I have a notion to go shopping" might be said to by a wife to her spouse, meaning roughly "I think I will, unless persuaded otherwise.")