Where can combat dice and extra units be bought?
There are various places you can shop online for spare pieces.  One such location is at http://www.historicalboardgaming.com/Axis-Allies-1941-2012_c_196.html

Alternatively, simply getting an additional copy of the game from a yard sale might be more cost effective at times.

As for dice, to my knowledge they are standard d6 with a special symbol in place of the 1, but functionally they are the same otherwise.  I have been very pleased with the quality of dice from http://www.chessex.com/ and I regularly visit their booth at conventions.