As a general rule, your CV should reflect both your strengths, in decreasing order, and the strengths that your target audience is looking for, in decreasing order. If those two priorities don't coincide, you may not be a good fit for the position.
From the list in your question, I would guess that you have more teaching experience than research experience, and that you value your research record (= publications) less than your teaching record or your "computer skills". This may be appropriate for a teaching-oriented position (in particular, one where you are teaching "computer skills"), but it's exactly backwards if you are aiming for a research-oriented position.
Assuming you're applying for a research-oriented postdoc position:
Personal information, including your work and education history, must come first, because that's standard, and you don't want to give anyone an excuse to think before they read the content.
Awards next (if you have any), because you want to convince people that you're good at what you do (or at least that other people think so), even before they read the actual content.
Publications next, because that's all that a majority of the hiring committee cares about. Be sure to distinguish invited papers that carry extra prestige, because you want to convince people that you're good at what you do, even before they read the actual content.
Then grants (if you have any), because the people hiring you want to know that you can get money on your own. This is less important than your ability to publish good research, but more important than....
Everything else, with whatever is more impressive and/or relevant for your desired position first: Presentations, teaching experience, advising/mentoring experience, community service (conference committees, refereeing, ...), university service (serving on an admission committee, organizing a seminar, ...)
References at the end, if and only if the position requires references in the CV itself.
I would omit "computer skills" entirely, unless those are actually the skills you want to be hired for. (Then again, I'm coming from computer science, where "computer skills" are so necessary (and therefore boring) that actually mentioning them is weird. Your community may have different expectations than mine.)