all of them are slang talk to mean that you did well , like the other user said it, should be said between friends

All four mean to do something exceptionally well. They are all very familial and colloquial terms. I would say personally that "nail" and "kill" are most commonly heard. I rarely hear "slay" here in Australia. Maybe more American? I hear "crush" most often used in reference to an easy sporting win. E.g "How did you go in football today? We crushed them."

Yes Ethan, they all mean similar things "nail" is usually more directed, as in "i nailed this interview" "crushed" is usually more general "how's your job?" "Im crushing it". None are offensive, but you wouldnt say any of these in a workplace