We have had possession pay our rent on time and everything. Do the people who own the house have the right to put their house up for sale and show it while we are living here?
I am disabled and this can be very life interupting at times please help? Do they have a legal right to show it while we are here and will our lease agreement be annulled when they put it on the market?

Yes, they may put the house up for sale and they may show it, It is Their house. They merely are suppose to give you proper notice, ( normally 24 hour notice they are showing the house.
No the lease is still valid, and if they sell the house the new owners will be the new landlord and have to honor the lease.