I completed the "How little we know" quest a while ago where you choose to either help the Omerta bosses or help Cachino overthrow them. Since I didn't like Cachino very much I decided to help the bosses but it turned out they were on Ceasar's side and were hell-bent on destroying the Strip. I am not a friend of the legion and have decided to go with Yes man. Since going with Yes man essentially means taking over New Vegas by yourself why on earth would I want the Omertas going on a killing streak in my own place?

Basically what I'm asking is how will this affect the rest of the game and the ending, preferably with as little spoilers as possible.

take the Omertas out. All of them. With extreme predjudice

But will that fix the problem of Yes man saying I approve of them taking out the strip? I read that it didn't and it's too late even if I kill them all myself. This was 20 hours ago and I don't feel like backtracking that far and I'm cautious about editing the game myself.

It really irks me for some reason.

if you remove the Omertas, then they can't take out the strip afaik. (Make sure you get the "civvies" working for the Omertas too, up in the suites)