There has been outage in my house for the past 8 hours.
I want to know if there's a better way of saying it or if this is grammatically correct.
"Outage" is something the service provider would normally use:
We are working on an outage in your neighborhood.
The customer would normally use "out" or "down" depending on the service:
My power's been out for 8 hours.
My internet's been down for 8 hours.
If we change "outage in" to "a power outage at", the sentence becomes grammatically correct.
There has been A POWER outage AT my house for the past 8 hours.
That still sounds a bit odd though. Usually a power outage refers to everybody that lost power, not just your house. I think this sounds better:
There has been A POWER outage IN MY NEIGHBORHOOD for the past 8 hours.
I also like boatseller's answer. He gives the more colloquial way to describe a power outage, using the phrase "the power's out".