El, Elah and Elohim were commonly used by the Jews. The *Hebrew root word Alah means a rude deprecating remark, the root word elah means mighty oak or other strong tree. Alah can also mean leaf, top of the tree, and the mighty one. The root word Allah means attacked by (usually) a mouse. These words (in Hebrew) can also mean God. It's just a theory but I wonder if that is because the Jews, Arabs etc used to live together pre-Mohammed and the meanings of the words became mixed in.
The Arabs used the word Allah before Mohammed for their 'Top'god, when Mo. introduced Monotheism to a Pagan audience he simply used a word they already associated with a 'main' god, he just got rid of the other gods/esses or 'partners.
I myself don't feel their 'Allah' is the same as the Christian/Jewish God as what Allah teaches is very different in morals/creed. Mohammed used to recieve revelations regarding robbing caravans, killing prisoners, raping women prisoners etc. Allah also seems to spend an inordinate amount of time making sure Mohammed gets what he wants. Every time Mo breaks a law, he gets a revelation, even an abrogation! if thats what it takes to keep him happy. There is even a surah where Allah appears to 'wait' to talk to Mo. before deciding something.
*Strongs Hebrew Dictionary.