by my great strength and my raised arm

The phrase "raised arm" refers to great power and intensifies the first phrase. Alternate translation: "by my very great power" (See: rc://en/ta/man/jit/figs-idiom and rc://en/ta/man/jit/figs-doublet)

I give it to anyone who is right in my eyes

Another possible meaning is "I give it to anyone I want to."