According to what I understand, and, as someone above pointed out, if you are living abroad, then, technically, while you are still a US Citizen, you are no longer a resident of any state in the US. When abroad, no one has every asked me for any STATE Identification; they only care about the passport which is a national form of identification. Therefore it seems that there would be no reason to even have a drivers license from the US when you are living overseas as long as you have your valid passport, and whatever visas are deemed necessary.
As for driving when overseas, each country has their specific rules as to what form of licensing you need, and, you should be able to get some form of license where you are. You should also be able to get an International Drivers Permit for use in the US and other countries. Other than that (and, for the purpose of maintaining an address in the US for other reasons) there is no reason to hold a drivers license from any state in the US. As far as voting goes, I would check with the US Embassy in the country you are living in as there are special procedures for that, and these procedures are constantly changing (more than likely, if you are permanently living in a foreign country, you will only be worrying about the national elections.).
Keep in mind that the problem with the US is unique; we are basically 51 (52) separate countries under the same flag with 51 (52) completely different sets of rules. Every other country in the world has a national identification card, and a national drivers license, and they also keep vital records, such as birth, death, marriage, and divorce on a national level. The US is the only country where each separate state issues identification; drivers licenses; and even keep their own vital statistics records, in whatever format is customary for the individual state, and, some states even require you to pay a state income tax.
As an example how this can be somewhat of a problem, a number of countries even require foreigners to submit proof from their governments that they are eligible to enter into a marriage when getting married overseas. The US is the ONLY country unable to provide such a document since everything is handled on a state level. So, the embassies/consulates have to provide an Affidavit in Lieu of... document, that not every locality will accept.
The only foreseeable problem with having an expired drivers license from a specific state in the US is that, when/if you go back home, and attempt to renew the license, there might be late fees and reinstatement fees applied. But, as the US allows people to drive using an International Drivers Permit, there should be no problem unless you are planning on renewing the state document.