Neither Henry nor his sons have a Prius (sons is plural and is closer to the verb than Henry is)
Neither the boys nor Henry has a Prius (Henry is singular and is closer to the verb than boys is).
If you believe that have sounds better, Chicago suggests arranging the sentence so that a plural noun is closer to the verb than a singular noun (Neither Henry nor the boys have a Prius).
And of course, not everyone abides by the Chicago Manual of Style. Other authorities say to use the plural form of the verb when any subject in a sentence is plural. (Link provided by Ted Dorsey.)
Tara’s Writing Studio