The radio will use energy to push the coil attached to the speaker diaphragm by pulsing through the electromagnet. A larger speaker with a larger electromagnet will therefore draw more current from the battery as it pushes a larger coil.

So the tiny earphones will provide the longest battery life as opposed to the larger headphones.

The volume at which you play the radio will make the largest difference in battery life - as the amplifier circuit is adjusted by the volume control knob and permits more electricity to be consumed.

Your best bet is to find a portable that can run on AA lithium batteries and keep some spare ones handy, as these batteries really do outlast conventional ones. They also sell hand crankable emergency am/fm/sw radios that can be recharged by hand.