Do we have the power to kill an Old God? Yes. Beating something into submission (which is apparently what we are doing for you) equals to us being as strong as them. Defeating is often used interchangeably with killing. We fight them directly, and succeed. Why wouldn't we be able to kill them?

We've fought and "killed" several beings in the game, but they did not actually die, or they did not die by our hand. Garrosh and Gul'dan are the most recent examples. Gameplay =/= Lore.

You see Echoes of Arthas throughout Legion, yet you don't say he is alive at all. You know we killed him on top of ICC.

Are you really comparing Arthas, a mortal, to giant parasitic beings created by godlike entities that can't manifest in our own world?

Since they are made of Saronite, the blood of a dead Old God

Except it's not the blood of a dead Old God? Icecrown Citadel was created out of the stuff, and you find it all over Northrend before we even knew about Yogg-Saron.

Y'Shaarj is totally dead, yet he kept us busy for a whole expansion. Dead Old Gods can still influence the world around them. For instance, the mere presence of the Heart of the Y'Shaarj caused a group of Aqirs to eventually become the Mantid.

Yes, but the only intact piece of Y'shaarj that was left was the Heart. We haven't seen any bits of Yogg laying around other than saronite, which existed and was used before we knew about him.