Spray methyl anthranilate on and around your stucco overhang. This is a grape flavoring that certain types of birds do not like to be around. This may deter the birds from continuing to spend time and nesting on your property.
Use a noisy scare tactic to spook the birds from your overhang. There are many different types of noises that birds are frightened by including firecrackers, propane cannons, gun shots, birdcalls and ultrasonic noise machines made specifically for birds. Only employ methods of this type that are legal where you live in order to avoid problems. Items made specifically for birds can be found at sporting goods or hunting stores.
Place visual deterrents on or near your stucco overhang. These include flashing lights, flags, balloons, fake birds, aluminum pie pans and scarecrows. Leave these items in place until the birds are gone and use them again if birds come back to try to nest. If they do not work within seven days, try another approach.
Protect your overhang after the birds are gone to prevent additional birds from roosting or nesting. Place netting, canvas outdoor cloth or chicken wire over the overhang's opening if it is not too unappealing visually. If it is, place a chemical bird repellent on the overhang. Because birds dislike landing on this sticky substance, they will go elsewhere in the future.