Which organisms are extremely small and use hosts as both home and food supply?

I would say that the bacteria who live inside one's gut would constitute very small organisms that are extremely small and inhabit the gut as home and also feed off it to survive and in this case probably have a symbiotic relationship with our bodies as they help us to break down and digest food.

Parasites

Explanation:
Parasites are a type of pathogen that survive by hitchhiking a host. They usually do this as they perceive the host as type of protection for them in order to survive.

Beside this protection, the host provides these parasites with the necessary nutrition as they feed directly from the host.
They can feed on different parts from the hosts including:
1- the digestion as in case of tapeworm
2- brain tissue as in case of brain-eating ameoba
3- blood

Parasites' presence in the host's body can alter the functionalities and processes within the body and cause sickness.

Hope this helps :)