My cat vomit his food on rug and I spill oil the other day.
Here are some tips https://www.thespruce.com/how-to-clean-a-wool-rug-4177780
Nature’s miracle in the red jug will get pet stains and their odors out. I use brake fluid cleaner in the spray can on oily stains. Use a clean rag to wipe up towards the center of all stains. Use plenty of ventilation. I also lay a clean cloth over the spot do it can dry without foot traffic.
Hi Jessica: Here are a couple of sites for the vomit:
here is one for oil:
Hope kitty is feeling better.
Try Simple Green. It's a degreaser/cleaner that is non toxic and works on a lot of different soils.