If you hold Indian passport and a valid US visa than a transit visa is not required in all cases including transit thru Europe.
If you don't have a valid US visa then you can travel transit visa free thru Singapore, Hong Kong and other East Asian hubs (as long as you are not going out of the airport). You will need a transit visa thru most European hubs. I think dubai allows transit visa on arrival for 48 hours. (Check with Emirates)
EAD has nothing to do with travel. In order to return to US you will need a visa or a valid AP.