1) There wasn't a gun in the house.
2) There were no guns in the house.
3) There weren't any guns in the house.
Is there a difference between the meanings of these sentences?
I think we get less dramatic as we move down!
I think '1' gives the impression either that 'a gun' was expected, thought, suspected to be in the house, or that the speaker wants to emphasize the fact that not even a single gun was in the house.
I see no significant difference between the three.