You only need to test with five users. That's an oversimplistic point, and need is the key word, but the important point is that you can easily find most of the major issues with a small sample set. I think seeking statistical validity has you going down the wrong path.
You're not conducting peer reviewed research, you're conducting iterative tests on a single product. You don't need something you can run once and be 100% sure about, you should running tests every step of the way.
If you can't get five users each step of the way, test one user1:
As soon as you collect data from a single test user, your insights shoot up and you have already learned almost a third of all there is to know about the usability of the design. The difference between zero and even a little bit of data is astounding.
Steve Krug's Rocket Surgery Made Easy describes great ways to conduct quick, simple usability tests on the cheap, without professionals. Again, these won't catch every possible usability problem in one go, but they'll allow you to test repeatedly to catch new usability problems introduced or uncovered after design changes.
From the description, Krug's book can (and will) help you:
- Test any design, from a sketch on a napkin to a fully-functioning web site or application
- Keep your focus on finding the most important problems (because no one has the time or resources to fix them all)
- Fix the problems that you find, using his "The least you can do" approach
Note for statistical validity you'll need a nice large sample, ideally of at least 30 so you can normalize results. Statistical validity is usually not a priority unless you're doing a simple survey as it requires a relative large number of participants for simple usability tests. Do not focus on this.
For specific tools, Usaura is a great quick and free resource to let you send quick tests to users over the internet. Note they don't let you test live interfaces but you can do some quick A/B testing on a visual layout of a page, ask some quick questions, or get a click map of where users think "where should you click to do...".