Rental home... Outlet under propane gas stove is facing up and when my son accidentally knocked over a glass of water (4 oz) it dripped down to outlet and is now making a clicking sound. No breakers tripped. WHAT TO DO? Landlord won't help

An electrician will turn off power to that circuit, remove the receptacle, clear out water and dry out, then install a new receptacle.
A weather proof cover may be a good idea.