Now, as Saudi Arabian Airlines has decided to join Skyteam, so Oneworld's share in Middle East is weakened. So, should Oneworld invite these airlines to join so as to improve competitiveness with Skyteam?
1.EK (Emirates)
2.QR (Qatar Airways)
3.EY (Ethiad Airways)

OW could invite those carriers as much as they want, they wouldn't join. Especially not EK or EY.

Correct , the question is not if OW wants EK or EY to be part of the alliance.

Why do they need to join an alliance? The gulf-based airlines already are super connectors.

Wishful thinking but I certainly wouldn't mind Emirates being a part of OW

What about Gulf Air, wasn't there a rumour that they had a possiblity of joining OW. They might not be in he same league as EK, EY and QR now; but they still have a large number of regional flights that could expand OW network into the middle east.

1.There were also rumours that QR had Star Alliance as their favourite choice between the 3, so we can rule them out.
2.EK said that they have no interest in joing any alliance, so we can rule them out.
3.EY now has a strong connection with DJ and VA. Rumours have been going on that EY wants to buy a stake in VS, if VS creates an alliance I can see EY joining them in the near future. So we can also rule them out.

Looks like all 3 major airlines have chosen their own way; i can't really see EK and EY joining any alliance in the near future, the only one I can see is QR who wants to join SA.
If the 3 major airlines have chosen their own way, the only good airlines left are GF, WY, LY and AT. And it looks like GF might be OW choice