Technically, regular humans can defeat monsters, if they have access to Celestial Bronze or another blessed metal. We see this with Dr. Chase at the end of The Titan's Curse:
Just as the army of monsters came over the hill, a Sopwith Camel swooped down out of the sky.
"Get away from my daughter!" Dr. Chase called down, and his machine guns burst to life, peppering the ground with bullet holes and startling the whole group of monsters into scattering.
"Dad?" yelled Annabeth in disbelief.
"Run!" he called back, his voice growing fainter as the biplane swooped by.
The Sopwith Camel swooped down again. A few giants threw javelins, and one flew straight between the wings of the plane, but the machine guns blazed. I realized with amazement that somehow Dr. Chase must've gotten hold of celestial bronze to fashion his bullets. The first row of snake women wailed as the machine gun's volley blew them into sulfurous yellow powder.
Percy Jackson and the Olympians, book 3: The Titan's Curse, chapter 17: "I Put On A Few Million Extra Pounds"
Titans; probably not.
Titans is a bit of a harder question; I'm tempted to say no, as you need godly forces battling them to be able to combat the Titans' own powers. As we see in The Last Olympian, Morpheus is able to put all the mortals to sleep, but the demigods remain awake. You'd need some godly power on your side to be able to defeat them.
As for the giants, definitely not; you need a demigod and a god working together to defeat them, and they also have powers akin to gods and Titans. The giants would be able to break out; they can't really be contained, even by demigods.