Some userfull Exim command:

exim -bpmailq --- The mailq is relevant as it gives your the email IDs.
exim -M emailIDforce delivery of one message
exim -qf Force another queue run
exim -qff

Force another queue run and attempt to flush frozen messages
exim -Mvl message IDView Log for message
exim -Mvb message IDView Body for message
exim -Mvh message IDView Header for message
exim -Mrm message IDReMove message (no errors sent)
exim -Mg message IDGive up and fail message, message bounces to sender