Joel,
Pics #3 & #4 are poison ivy. You remembered "leaves of three, let it be" in #1 & #2 which is a good general rule if you're not familiar. Poison ivy starts purplish and shiny then goes green. Its three leaves might have a cleft on one edge of a leaf but not always. The berries in the fall are toxic too. Be REALLY carefull mowing as the mulched up plant coming out of your chute will be like a bee attack in a couple of hours.
AFAIK the only way to kill it is to spray Ortho Brush Be Gone. Cutting won't do it.
If you contact it by accident, wash with a dish soap like Dawn to remove the oil from your skin within 10 minutes. Don't scratch your skin. Calamine lotion will ease the itching if you're too late.
btdt.