I over pronate as well. You need special shoes designed for your type of pronation (under or over). The aren't all that expensive as far as good running shoes are concerned, but expect to pay $60 to $100. It's money well spent, running with shoes that don't work for you can lead to all kinds of hurt. (ever had shin splints?)

Cycling has never been a problem for me as long as I keep a little extra float in my pedals (when using clipless) and have my saddle height adjusted properly.