I think that it's important to first define what these three terms mean:
1. Teaching Approaches: I would say that this is the your own personal philosophy of teaching. What is the nature of education? What is the role of the teacher, the student, the administration, the parents? To be an effective teacher, does one need to strive to be authoritarian, to be autocratic, or is the best way to engender a sense of trust and familiarity, to be a 'educating/leading friend' to your students. To understand one's personal teaching approaches, one must first look to answer these types of questions. And of course, your opinion will change as time goes on - and it may vary depending on the students you're teaching.
2. Teaching Method: Refers to how you apply your answers from the questions stated in Teaching Approaches to your day to day instruction in front of your students. Do you follow the textbooks and curricula to the letter with everything? Are you more of a Socratic teacher and prompt discussion by asking questions to lead students to understanding? Do you advocate learning by doing? Are your students expected to simply listen attentively and take notes (not that any student really does that) with the hopes that they can memorize the facts for assessment? This is not really a question of 'what works for you' but what actual practices and procedures of teaching do you prefer and come most naturally to you?
3. Teaching Techniques: These are the little sneaky tricks we all know and use to get the job done in the classroom. Teachers all over have systems of rewards/punishments for students who comply and exceed or defy and lag behind. If a classroom is becoming distracted a teacher may use the technique of silent reading or shared reading to try to rope them in again. Another may choose to use a quick physical activity to distract their distraction and get them all to do the same thing at the same time - then quickly direct them back to work. This is really where someone with loads of experience can help another teacher improve her abilities. These are the tricks that can be taught to another teacher. Sort of "I find this really helps during math class" type of suggestions. Also a lot of the in-services and workshops all teachers attend offer little tidbits of games, activites, and actions that teachers can use to achieve certain goals in the classroom. Everything from sending a note home to mom and a trip to the principal's office to giving out 'points' for good behaviour are examples of techniques teachers can use to keep ahead of the pack.
I hope that this is what you're looking for. Well it makes sense to me at any rate. As important it is for a teacher to be able to talk about these things and understand the definitions and their impact on our craft, its debatable whether it is of any practical use to a teacher in front of 30 kids trying to teach common denominators or the causes of the First World War.
I'm in my sixth year teaching. I've taught on 3 continents in private/public elementary/junior/high schools to 4 year olds up to 18 year olds in everything from Studies of Religion to Mathematics. But I'm still learning (and trying to land a new full time job)