“living souls.” The Hebrew word “soul” is nephesh (#05315 נֶפֶשׁ), and nephesh is the life force that animates humans and animals, and it is also used of “individuals.” See commentary on Genesis 1:20. For more information, see Appendix 7: Usages of “Soul.”
“livestock.” In this context, this refers to domesticated animals. When God created the earth and humankind, and created the animals and birds to support, sustain, and beautify the earth, He made a distinction between the domesticated animals that would serve humans in various ways, and the wild animals that generally cannot be domesticated, and today, thousands of years later, that distinction still holds true.
“creeping things.” Or perhaps, “crawling things.” This is very general and generally refers to small animals and reptiles. Apparently it can also refer to insects, worms, etc., but that may not be its meaning here.