MTG Salvation

If I cast Inverter Of Truth and put the etb on the stack then, use Brain in a Jar to cast Harmless Offering can I stack the etb trigger happen after inverter has been donated to my opponent?

Brain in a Jar

No, and you have already stated the reason why. You aren't casting Harmless Oferring until after you put the EtB trigger on the stack (this is the first opportunity you have to respond after Inverter of Truth resolves) and by then it is too late.

In this case, you will control the ability as you controlled the source when it triggered. You would have to find a way to "donate" the Inverter of Truth while it is still a spell on the stack and outside of Mindslaver/Desertion shenanigans, I am not sure there is any way to do that.

Ok, I'm a magic retread I've only been back into the game a short while with that said how is it possible to kill an Avacyn at instant speed before the etb resolves but not shift possession of this creature also at instant speed am I missing something? If i cast Avacyn and she gets killed on etb are my other creatures still indestructible?

Yes, your other creatures are still indestructible in that case. Removing the source of a trigger does not (generally) affect whether that trigger resolves.

Also note that no matter what, if you control the source of the trigger when it triggers, you also control the trigger (which is the case in original question). The same goes for Avacyn. If someone steals her in response to the trigger, your creatures still get indestructible.

Awesome man, you cleared up a ton of timing issues with etb triggers thanks from my play group!