You should be able to enter your corporate number on Expedia or Orbitz. Sometimes you have to run your global search first, pick the company you want to use (from the list for which you have valid corporate numbers, of course), then re-search for your company specifically using the corporate number.

The only catch is that you can't use a different membership number to get a lower rate, and then still get your under-25 benefit from your corporate code. For example, you can't use the Costco or AAA rates and then use your corporate code at pickup. But since you are using Expedia or Orbitz you are just getting generic rates for the most part anyway, this shouldn't be a problem.