Here "lusts of their hearts" is a synecdoche that represents the evil things they wanted to do. Alternate translation: "the morally impure things they desired greatly" (See: [[rc://en/ta/man/jit/figs-synecdoche]])
This is a euphemism that means they committed immoral sexual acts. You can translate this in an active form. Alternate translation: "and they committed sexually immoral and degrading acts" (See: [[rc://en/ta/man/jit/figs-euphemism]] and [[rc://en/ta/man/jit/figs-activepassive]])