Over-oiling is better than under-oiling, as 3alarmer said, excess just leaks out.
You may wish to flush the hub with white spirits (or whatever they call it in the US), to remove any gunk from it before adding any new oil.
Also, although Jobst Brandt has something against the Sturmey-Archer AW, bear in mind that the failures he describes occurred mostly under extremely hard riding. They're fine for regular use.
Finally, it's spelt Sturmey-Archer, although it's often rather hard to read the stamping on the hub shells to be fair.