The salesman did not ask if I had ever used self storage before. He did not mention either the free gift or invite me to visit a location.

The salesman did not ask whether I had ever used self storage before. He did not mention either the free gift or invite me to visit a location.

This can be considered style preference these days - the word 'if' is acceptable to many.

The last sentence is non-parrallel. This means that you have different structures in a list.

He did not mention either:

the free gift (noun) or:

invite me (verb).

You can get around this two ways:

He did not mention either the free gift or an invitation for me to visit a location.

Or simply:

He did not mention the free gift or invite me to visit a location.