The name of the most ancient Greek goddess Gaia has strong resonance in Basque language, where gai(-a) has several interrelated meanings:
- Most basically gai(-a) means substance, matter (incl. the matter of a discussion or a lesson, for example)
- Gai also means able, capable: gai izan: to be able. Gaitasun (quality of "gai"): potential, capability.
- As suffix -gai(-a) means also potential, for example ezkongai: fiancé(-e), bride or groom.
Therefore, if Vasconic, the divine name Gaia has a lot of meaning consistent with its mythology as mother goddess identified with Earth.
ITSASO (sea), probable cognates Greek THALASSA, Germanic SEA, ZEE, etc. In the first case we notice the similitude mostly from the suffix -ASO, in the other it is the root *IZ- ("water" most likely), probably in the basic nominative form of *IZA or *IZE, the connector, while the respect suffix -ASO is either lost or was never used in those parts.
As for Greek THALASSA, there is clearly an extra element -al- when comparing with ITSASO. Maybe it was the word ahal = might, power, can (verb). If so the original Vasconic word would be *IZ-A(ha)L-ASO(-A), i.e. "the venerable power of water".
OIKOS (often pronounced EKOS, root of our common eco- particle, as in economics, ecology, etc.), meaning "house" or "home" is similar to Basque ETXE. The X is probably a diminutive or appreciative element so we can think of a root *ETZE instead, plausibly related to the verb ETZAN (to lay down).
OKHI ("no") and NE ("yes") are totally non-IE Greek words. OKHI can be compared with Basque EZ, following the same kind of phonetic change as *ETZE. This seems totally regular, what is always a plus. NE is a bit more unclear but I'd propose it is related to Basque BAI (by a separate derivation could also be related to Slavic and Romanian DA: "yes", which in turn might be related to Basque DA: "it is"). Greek is the only IE language AFAIK that does not use N- (ne, no) for the negative particle but does instead for the affirmative one, extremely strange and most likely a pre-IE legacy in any case.