CA-1-B16 Question

Any mains voltage rated two core flexible cable of similar gauge, with a black outer sheath is suitable. Someone more local might be able to be more specific re an actual supplier, since things are different in my part of the world.
Keep in mind that the wiring inside the cabinet top will be in similar condition, and should be replaced also.
The two pin locking plugs are unique to GE and a new replacement would be impossible to find. The inline plug for the light socket was being reproduced by a forum member, but that was a long time ago. A two pin extension cord socket will fit, provided the diameter is small enough.
As with any newly acquired CA, the oil heater needs to be tested before it's put into regular use, and also it needs to be tested for NCG's and purged if necessary.