It depends what level you want to work at, as to the experience and education you need.
If you want to work at the collegiate level or with a professional sports team then it will be required for you to have at least a bachelors degree in a field related to exercise science. Most colleges now require a Masters degree to be a head strength coach (at least at Division 1).
In addition to a degree, you will definitely need experience at the level you want to work at. Experience at the college level can be obtained through volunteering (at first), as a graduate assistant, or starting at a smaller school. Most colleges desire some experience prior to hiring.
If you want to work with a professional sports team you will need some experience at the college or professional levels. Experience can be obtained through the same way as college experience.
Most colleges and pro sports teams also desire a certification. The most prevalent certification is the CSCS (Certified Strength and Conditioning Specialist). To take the CSCS exam, you must have a bachelors degree (the field it is in does not matter).
Seminars and real-life experience really don't matter when applying for a job. They may matter when looking at how successful you will be on the job, but from someone who has hired in the past...I really don't care what seminars you've been to.
Now, if you would like to be a private strength coach or work with high school athletes then the above does not apply. You can get by working with lower level athletes without a degree, without experience, and even without a certification. Although possessing degrees, certifications, and experience definitely helps.
Last important point, it really does help to know people in the strength coaching industry. As with any field, the more people you know and the more people you have worked with dramatically increases your chances of success.
In order of importance (at least in my opinion):
1) career experience (very hard to get without a college degree).
2) college degree
3) who you know
5) real-life experience
6) seminars attended