Nigel says: I suppose it depends what message they wish to put across.
It could be either:
"The Strongs live here" in which case I assume you wish to delete the apostrophe.
Or, "This is the Strong's house", which, as a label, I assume you would wish to add an apostrophe after "The Strong's" to show the ellision of the word 'House'

In the second instance, your sentence should read "This is the Strongs's house" and therefore you would want the sign to read "The Strongs's". However, such a sign traditionally denotes "The Strongs live here", so the sign should read "The Strongs" with no apostrophe at all.

The only way that the sentence "This is the Strong's house" would make sense is if the house had a single resident known as, say, Erik the Strong and if the locals referred to him as "the Strong".