Paragraph Styles are for whole paragraphs.
Character Styles are for single words or letters. Don't use the along a whole paragraph. Don't define all attributes, only those who are different to the properties of the Paragraph Style. Contrary to Quark Xpress, in InDesign are Character Styles used only for the difference for single words.
Paragraph Styles can include Character Style in an automatic way: GREP Styles, Nested Styles, Initial Letters, automatic bullets & numbers and line styles.
Object Styles define the Object, the frame. They include separate definitions for the whole object, the stroke and the fill.
Object Styles can also be applied to images in a frame and for groups.
Object Styles can also include in an automatic way Paragraph Styles and the next Paragraph Style.
Object Styles have several categories, you can choose which category is relevant to be applied. It is e.g. possible to apply the first Object style to give stroke and fill, and the apply another object style to format the corners only and then apply the next. (With this method only the last applied Object Style is linked.)
Styles give the opportunity to make global changes in a document. If you build them up in an intelligent way they are an enormous time saver. They can be stored in CC Libraries or in Libraries with Objects applied to them. If you have created once those styles, you can use them again, and with one or two clicks you can make them fit for any new document.
My recommendation: Become used to Styles, name them always with the same names as it helps you to be acustomed to them and to work faster, much faster.
There are more styles: Table Styles, Cell Styles, Master Pages and Swatches.
Paragraph Styles are for saving the text formatting of entire paragraphs. Paragraph Styles will save any of the formatting you can apply in the Paragraph panel, the Character panel, as well as type color. Paragraph Styles are your main text formatting Styles applied to all text in your document.
Character Styles save character formatting only (formatting found in the Character panel as well as character color). Character Styles are used to apply character formatting to a portion of a paragraph that is different than the character formatting formatting found in your Paragraph Style. For example, you would like a movie or book title to be formatted in Italic. Save a Character Style to change the selected text to Italic. If you wish to change the character formatting of an entire paragraph, create a NEW Paragraph Style instead of applying a Character Style a whole paragraph.
If you "format" an object with a certain Fill, Stroke, Effects and other options, the look can be saved as an Object Style.
For more, check out the following video tutorials: http://www.jeffwitchel.net/2013/08/indesigns-super-styles/
Great book Bob!
Thanks a lot everyone for such an overwhelming amount of helpful replies in such a short span of time period.
Bob recommended Michael Murphy's book on InDesign styles.
See also his website with some helpful videos mainly revolving around InDesign CS3 to CS6:
Especially see his video series about Nested Styles there.
Unfortunately Michael stopped recording videos around 2013.
One was following in 2015 about GREP.