Hi Mjk
My interest in the powers was initially quite the opposite of yours: I thought they were all about Woo-woo. Since starting a dedicated meditation practice a few years ago, I've had my share of weird experiences that might qualify as the powers manifesting.
Like Daniel wrote in the other thread, the powers are endlessly fascinating. Doing insight practice is really drab by comparison. If awakening is your goal, that's a good thing to keep in mind, along with the fact that the ability to display powers is no indicator of a person's progress in insight. On the other hand, entire traditions use the powers as their main practice for gaining insight, such as Western Magick, Vajrayana.
Another thing about the powers: trying to understand them in terms of "reality" or "laws of nature" is not likely to be helpful. They do have a kind of "causality" going, but not on a mechanical/physical level. Thinking in terms of "change" or "synchronicity" or "narrative" or "meaningful coincidence" or "this happens along with that" or "this leads to that" is more useful. Again, IMO. The other side of this particular medal concerns "means of manifestation": If you want to use the powers to fly, you'll have to do so in a lucid dream, as physical reality won't permit you to. Daniel does a great job discussing this in the chapter on the powers in MCTB. You might also want to check out Alan Chapman's "Advanced Magick for Beginners" for a really good read (and many useful practice suggestions) on the subject.
So - all of that said, here are some experiences with the powers. Don't expect anything spectacular, though. Much of it is a matter of interpretation. The experiences can be very compelling, reading about them won't convey it too well, I guess.
Out-of-body dreams/experiences. I've had a few dreams featuring elements common to descriptions of "out of body experiences" such as the noise and wrenching sensations at the beginning/end, sleep paralysis, the sense of another "presence" close by (commonly interpreted as the "other" body), a pull or strong current or wind, which is also audible; then the grainy sense of sight, numbness when touching things. Of course, some of these elements are also common to descriptions of the "night hag" type of nightmares. In a typical example of this power manifesting, I'd dream of a thunderstorm (noise), dream of waking up and going to check the windows of the house, in case one was open. I'd try to turn on the light in a room, fail for some reason, maybe ascribing this to a power failure, and in the dim, grainy vision I'd try to feel if the window was open. I wouldn't be able to feel the window very well, and suddenly I'd realize my arm was halfway through the window, or I'd think I broke the window. There would be a shock, a surging sensation, and I'd wake up in my bed, agitated, realizing there's no thunderstorm and so on. A milder form of this type of experience would be getting up at night to go to the bathroom, not being able to turn on the light (recurring theme, that), not being able to pee (lack of physical body, and a good thing, actually

), looking in the mirror and waking up from the shock of what I saw there, which I never quite remember. I used to dismiss these as unpleasant or strange recurring dreams, but reading up on OOB type experiences made me change my mind. They tend to occur when I'm in A&P territory, confirming the maps nicely - even looking back to before I knew about the maps.
2. Meditation experiences - these are mainly visions of places or objects or persons. After exiting a jhana state, the mind will often turn to whatever first pops up, which can be the most unlikely things: I've "been to see" the guy with the flashing eyes, flying hair out of Coleridge's "Xanadu" for example. Several times, a medieval castle or similar structure with dressed stone corridors, pillars and wooden doors, parapets, and staircases. I've "stood before" a being bearing the globe of the world, a bit like Atlas of Greek mythology, only upside down, so to speak. Actually, he then flung the globe at me, and I think that was my initial A&P crossing experience. Long time ago. Often these kinds of experience are preceded by an impression of velocity or "flying" (not height but distance). The Sutta formula of "a strong man flexing or extending his arm" is quite apt, I think.
3. Statement of intent. I mainly use these in the form of "formal resolve" when meditating. For example, when doing concentration practice, it's really awful to be interrupted by the meditation timer when in a jhana state. So when I have to use a timer (in the morning, or during lunch break at work), I make a formal resolve to enter jhana, and exit it just before the timer goes off. This kind of thing is really very effective. When doing insight meditation, I use formal resolves to go to the "cutting edge" of my practice, to visit a particular nana for a closer look, to get up only when the timer goes off (useful in dark night/reobservation), and so on.
So that was a bit of detail about my experiences with the powers. If you wish to access/explore this stuff, I'd suggest that you develop strong concentration. For me, kasina practice was surprisingly effective there. Experiment! Have fun. Don't confuse progress in the powers (and other concentration skills) with insight progress, not even if an impressive being in a vision tells you otherwise

Cheers,
Florian