How may theists respond to the philosophical 'Problem of Evil'?

The philosophical Problem of Evil is an A Priori argument (from definition/first principle). It states that it is logically impossible for the typical monotheistic God, presented by the Abrahamic faiths for example, to exist. If God is defined as being omnipotent and omnibenevolent (and omniscient), then He should want to prevent evil and suffering, and is able to stop evil and suffering, but both are still prevalent in our world, evidenced by the starving masses, rampant poverty and disease just to name a few. Typically, a theist would respond to the philosophical problem of evil by broadening the definitions given to compensate for the evil and suffering we see.
Two easy examples to note would be the Augustinian response and the Irenaean response. Ireneaus presented the Free Will defence, an argument that broadens the definition of omnibenevolence to a sort-of tough love. He argues that moral evil, committed by humans, must be necessary as to morally develop we must be capable of making wrong decisions. Natural evil, like disease or natural disaster, is the necessary context to teach us what evil is. He redefines evil as not wholly negative, as it teaches us how to act morally and bring us closer to Gods likeness. Augustine redefines evil as the absence of good, as nothing created by a perfect creator can ever go bad. What we see as evil is simply our fault as well, after the fall of man and original sin. Therefore theists can respond to the problem of evil by broadening the strict definitions provided to let God "off the hook" so to say. However there are plenty of criticisms to these responses, so they are not foolproof.