Nashes or Nash’s??

The Nashes' house if you want to include the house, or just "the Nashes" if you don't.

Or "Chez Nash" if you want to be poncey.

To clarify that last comment, "Nash's" is definitely incorrect. "Nashes" is the only plural of "Nash," and therefore if you wish to make "Nash" plural possesive, the only correct spelling is " Nashes' ".

Or just call it "The Nash House" to avoid the whole problem.

"Nash" ends in a sibilant, that means that "Nashes" is the way to go. All english singular nouns ending in sibiliants /s/ /sh/ /z/ /zh/ etc, are so pluralized.

There seems to be a confusion between plurals and possessives here. As a family, you would be The Nashes. If you want to talk about who's house it is, then it Nash's house in the singular, or The Nashes' house in the plural. (Or The Nashes's House--there are different styles on that last one.)

Is pluralizing a skill you develop the longer you've been married?

As a further clarification, "Nash's" would only be used when ascribing the possession to one person, and then only in conjunction with a first name or title, e.g. "John Nash's house". "The Nashes' house" would imply shared possession (check your mortgage papers).
"The Nash residence" would be a common-sense alternative that works either way.

Thank you for solving this lifelong puzzlement for me.