Spray a small amount of aerosol oil underneath the handrail where the arm coming from the wall contacts the bracket. Do each one. If the creaking persists, proceed to the next step.
Use a drill/driver to remove the two screws securing the handrail to the bracket. Measure the screws and replace them with screws that are 1/2-inch longer than the original screws. Hold one hand on the top of the handrail and apply pressure. Drive the new screws through the bracket into the original holes. Do all of the brackets one at a time.
Grasp the handrail with one hand. Attempt to tilt it back and forth. If you still hear creaking, proceed to the next step.
Remove the screws holding the triangular or oval bracket to the wall. There are two screws at the top, and one at the bottom. Measure the screws and replace them with screws that are 3/4-inch longer than the original screws. Drive the new screws into the original holes in the bracket to reinforce the wall bracket.