Afferent information is information that is inbound to the nervous system. Efferent information is outbound such as a motor command traveling from the brain to the muscles that will respond to it.
Local neurons are rather odd.
Local neurons are able to be stimulated virtually anywhere rather than just the dendrites or soma. In addition, they can conduct information in either direction not just away from the cell body toward the synaptic endings. They essentially are so short that they don't even have what might be considered an axon. Interneurons are also short but are more like traditional neurons. They are most often found interconnecting motor neurons in the spinal cord and are responsible for transferring the information that results in spinal mediation of motor reflexes.