Some of the words suggested are probably not connected. As far as I know:
Greek ouk is more likely to be ou + epenthetic /k/ before vowel. The other
form oukhi is ou + *ghi which is an emphatic particle (found in Skt after
"yes"!)
Latin haud is from *ghawo meaning false.
The Germanic words (kein, geen etc) are originally the same as Latin
ne-que-unus, so the velar bit is the usual word "and".
Hope that helps
Peter
> Latin - haud
> Greek - ouk
> German - kein
> Dutch - geen
> Icelandic - ekki
> Gothic - ains-hun
> Does anyone know the etymology of these forms? Do they all derive
> from a common PIE negative particle? Did this root occur at all in
> Old English?
>
> Brian