voltage regulators destroyed -- protection diode needed?
I'm guessing your switch was actually in position A rather than B in the diagram below (so it switched off the meter and Arduino too). If not, it's unlikely you could get 35V+ spike to kill the DVM and 7805 since the 24V battery would absorb it. If you have a bench supply or similar rather than a huge battery, then it could cause problems. 

In any case, a diode as shown will kill the inductive spike. Rating depends on the relay rating but a 1N5404 will work for just about any relay.