ADR's are not the same as trading international stocks in their respective exchanges. Asia, Europe, Middle East are mostly closed when US markets are open.
do you see any overseas markets that are day tradable? my reserch into Eupopian markets is that the stocks there is this tax based on the price of the stock that make kind of precludes making money day trading. i do understand that some ECN's are coming which might lower these fees.
Yo can trade them with Interactive Brokers, though you would need to pay for a feed for each mkt you want to trade. They're cheap, reliable and good. You can also use the feed to power your charts if you want to.