Chris and Suresh answer for research-intensive institutions. At a primarily undergraduate institution, teaching experience is more important, but search committees (being composed of people who went through the process before) know that most PhDs and post-docs have very little teaching experience, and most of it is the type that you have listed. What most committees are probably looking for is any evidence of teaching potential. Teaching experience does not always mean good teaching. If you do not have a lot of experience, then you should ask your references to address teaching potential in your letters (and you should have difference letters for primarily undergrad institutions than for research institutions).
Does more teaching experience help you get a phone interview?
Probably. It's one of the few things that can make you stand out on paper.
Does more teaching experience help you get an onsite interview?
No. Once you make it to the phone interview, it's all about you, your personality, and how you might fit with the department. In addition to teaching experience/potential, you need to show that you are interested and capable of starting a research program with undergraduates, and that you have a project reasonable to the resources of the institution. If your research requires use of one of only a half-dozen specialized instruments in the world, you will likely not get called back.
Does more teaching experience increase your chances of getting the job once you do the onsite interview?
No. The onsite interview likely will include a sample lecture. If you are interviewing at a primarily undergraduate institution, and you mess up the sample lecture, you're done. The sample lecture is how your teaching potential is measured. I've seen people with very little experience do a fantastic job (i.e. engage the class, work examples, answer questions, etc.), and I've seen people with 5+ years of experience stare at their PowerPoint slides, read them word for word, and never look at the class.