Can I use a 220 heating element in a 110 water heater as long as the wiring is for 220.
We had a 40 gal water heater 220 volts in a weekend cabin with one shower a complete over kill. Want to replace with a 20 gal 110 water heater but to take advantage of the 220 wiring can I just swap out the element and control only using the new 20 gal tank?

My honest advice is to leave it the way it is. Just turn it off if you leave the cabin for a long time. May be more than you need, but better than running out of hot water.

BUT

In answer to your questions.

1) A 220 volt element requires a 220 volt connection. Likewise, a 110 volt element requires a 110 volt circuit.

2) If you want to replace the water heater with a 110 volt heater, you should already have two wires running to the heater with a ground. One should be black, and the other will most likely be red or white, perhaps a white wire with a piece of black tape on it.

If it's a white wire then replace the 220 volt breaker with a single pole 110 volt breaker, connect the black wire to the new breaker. Then connect the white wire to the netural bus bar in the breaker box. If the wire has black tape around the ends, remove this tape.

Additionally, you can always swap the 40 gal with a 20 gal 220 volt. Then you won't have to mess with any wiring, and you get a smaller heater all the same..

Maybe. Is the thermostat 2 pole?

There would be no advantage to exchanging a 120V element to a 240V element unless the 240V is of high wattage than the 120V. If it is higher wattage it would mean a faster recovery but no energy saving.
The wiring to the heater can easily be converted to 120V. However, that will not result in any energy savings either. The only energy savings would result from the smaller size during long periods of inactivity.

KISS: Don't have a wiring diagram in front of me but I believe the thermostat on a 240V is single pole.

Here are some wiring diagrams that say 120 V and 277V. The stats look like two pole, but who knows how they are internally wired.

http://www.hotwater.com/lit/wiring/a7070.pdf

AO Smith says an actual wiring diagram is furnished with the heater. Looks like they don't make residential electric.

120/240 The difference is primarily reliability when you have a choice. 240 is better. Wiring still has to be sized properly.

But since the heating value of a particular current and a fixed resistor is I^2*R; suppose you have 1 ohm and 1 amp. I^2*R = 1 Watt. Now for 240 V; R is the same, I is 0.5 or half of 1 AMP. 0.5^2*1 = 0.25W or 1/4 W. If this was a contact resistance, then 240 V would be 4 times hotter. You want the lowest resistance across the contacts and the lowest current.