Where does an organism store reserves of the amino acids it needs to build various proteins it needs -- in the liver ? in the blood ? in every cell ?
In the sense that you have asked the question, humans have no stores of amino acids. Amino acids obtained from the diet are quickly incorporated into new proteins or are metabolised as fuel molecules.
Proteins are subject to continual turnover, and the amino acids that are released by degradation are either reused or metabolised in exactly the same way.
This is one of the reasons why the diet must contain appropriate levels of essential amino acids (those we cannot make for ourselves) since these are continually being released from proteins and used as fuel - we have no mechanism for storing them in case of future dietary deficiency.
During starvation the protein turnover process releases amino acids from muscle and these are mainly used as fuel molecules. This is why muscle wasting occurs in starvation, although the mobilisation of fat reserves helps to delay this as long as possible as tissues, including brain, switch over to relying on ketones (derived from fat breakdown).