Can an ordinary power drill drill through steel?
Most drill bits sold are "high speed" drill bits intended for a variety of materials including metal (but not concrete, tile, glass or extended use in plaster or plasterboard). 

If the bits are fairly sharp, you should be able to use them in the steel, assuming it is not a hardened alloy.  To improve your chances, a bit of oil or cutting fluid at the cutting point will help prevent overheating. Slower is usually better.

The rust probably makes the steel weaker and easier to drill.