The four terms you have given are related to chemical wastes in the following way:
Chemical wastes are generally non biodegradable. They either cannot be converted by organisms in nature into substances that are not harmful or the process takes a very long time during which the chemical wastes pose a lot of danger to all organisms that come in contact with them.
Landfills cannot be used to dispose chemical wastes. Doing so would lead to toxins entering the environment as harmful gases or into the underground water table. To dispose chemical wastes special storage facilities are required or landfills have to be altered to prevent the waste from spilling into the air or water.
Chemical waste left in the open can easily runoff and mix with the water supply when rain falls on it. They have to be kept secure from agents that can lead to their uncontrolled spread.
Chemical wastes usually cannot be incinerated as the gases produced contain very harmful chemicals. If they are being burnt, the gases also have to be treated in an appropriate manner.