I respectfully disagree. "I neither want nor need beer" . Here, 'neither' is associated with the 'want' not the object of the want i.e. 'beer'.
I neither want,or i want neither are the same in uk language
"I do not want either beer or wine"?
To my ear, "I want neither beer, nor wine" sounds very literary or archaic - it would be ok in: "I want neither beer, nor wine. Fetch me a flagon of the finest armagnac in Albion or I shall have you flayed!"