- I have no house.
- I don't have a house.
What's the difference between the phrases like the ones above?
The two formations are essentially identical in literal meaning, but the phrasing may be chosen for dramatic emphasis. Probably the most famous example of this construction is the cliched father who's disowned his child: I have no son! It literally means the same thing as I don't have a son, but it's much more emphatic.
Edit: The have no form, since it's technically correct but not used as often, is sometimes used for humorous effect to imply that English is not the speaker's first language. The most famous example is probably the 1922 novelty song Yes! We have no bananas.
Re-edit - updated YouTube link, as previous video had been taken down.
The answer is partly a trans-Atlantic difference, though less than it used to be.
Fifty years ago, when I was small, "don't have" was almost unheard in Britain, except in a habitual sense ("We don't have dances in our village hall any more"). Where Americans would often say "don't have", we would say "haven't", or "haven't got" or sometimes "have no".
When used as an alternative to "haven't a", "have no" is a little more emphatic; but in place of "haven't any" (eg "I've no money"), I would say it is completely normal for many UK speakers.
1- I have no house/s = I don't have any house/s. 1.1- I know nobody = I don't know anybody. 1.2- I see nothing = I don't see anything. 1.3- I am going nowhere = I am not going anywhere.
2- The word "house" (in this context) being a countable noun i.e., it may take the singular and plural forms. Singular: a) I don't have a house = I have no house = I don't have any house. (Three possible negative sentences) Plural: a) I don't have any houses = I have no houses. (Only two possible negative sentences because the indefinite article A,AN can only be used along with SINGULAR countable nouns)