Powering my Arduino Nano with 24 V DC
The most efficient solution would be to use a 24V->5V DC->DC converter.

Adding a 7805 at any point will simply waste power - the 7805 (or any other linear regulator) just acts as a resistor.  The current drawn from the 24 volt source will equal the current required by the Arduino (plus a bit for the regulator operation).

With a DC-DC converter, the power drawn (not the current) from the 24V source will equal the power required by the Arduino (plus a bit for the DC-DC converter operation and inefficency).