Squeaking = movement. However, simply screwing into a solid wood tread won't fix anything if the tread itself is flexing. If you have access under the stairs, you can glue and screw lumber or strips of at least 3/4" thick plywood under each tread to give it a thicker effective depth. Just make sure the screws aren't so long that they poke up through the top of the tread.
You can also use a heavy duty construction adhesive like PL 400 to reglue the joint where each tread meets the stringers.
