To me, offload means that the person is going somewhere. It is more than just dumping. If I dump a problem it means that I drop it entirely. If I offload a problem it means that I gave that problem to someone else.
"Dispatch" could mean "send" to me or, as xqby said, it could mean "kill."
 I suppose "offload" could be paraphrased as "dump a problem on someone else", but I wouldn't equate it to "dump" by itself.