It would be much easier for YOU to do a quick GOOGLE for each of the plants mentioned. All you have to do is type in (for example): boxwood propagation. Several authoritative sites will come up for you to read and glean information from.

I suggest that you use Latin names for a more acurate search. For example, in your location Yew is not used, but Podocarpus is called Japanese Yew. Is that what you mean? Tea Olive is Osmanthus fragrans. Banana shrub is Michelia figo.

I'll get you started with Tea Olive.

Here is a link that might be useful: Google search for Osmanthus fragrans propagation

I root a lot of rosemary. I don't do anything special except that I cut long stems rather than what some experts say. I don't use rooting hormone either. I take a plastic shoe box (the kind sold to store fancy shoes in) and drill plenty of holes in the bottom (don't worry if the plastic cracks in a few places). I fill it with regular soiless mix potting media. If I have any coarse sand or vermiculite I mix that in also - but I have done it without as well. I wet the media. I snip foot long lengths of rosemary and stick them into the media all the way to the bottom of the box - maybe 5 inches deep. I fill the box with as many cuttings as I can stuff into it. I set it in the shade and keep it slightly moist (I'll move it under the house eaves if we get a lot of rain). After a month or so I might move it into the sun but this has caused problems in the past. The biggest problem with rosemary is that it can take 6 months to get good rooting so you have to be patient. Usually fall cuttings are rooted well enough by mid spring. I take cuttings all year long and have the best success with fall cuttings that stay out in the weather all winter long. You'll know in a few months which cuttings took or not - the nonrooters will wither up.

My thoughts would be:
The woody stems root the best.
Longer stems give you a larger plant faster.
Don't use garden soil or regular potting soil - use a soil less mix instead (lots of peat moss).
Don't put them in the sun - bright shade is best.
Keep them just moist - don't overwater or allow to completely dry out.
Don't mess with them - be patient - when you see new growth on top, you know you have roots.

With Osmanthus fragrans, the best time to take cuttings is just as the new growth hardens in May or June. That's the time of year I've had the most success with rooting woody plants. Like John said, rooting can take a long time. I had piece of lilac from Witherspoon take over two months to put any roots out at all. And with some plants you can get top growth before root formation.

Rosemary is the one I have the best success with. My first bush I rooted from the garnish on my dinner at a restaurant! Since I grew it in a pot because of my heavy clay, it died after about three years because of lack of water while I was out of town. I replaced it with a plant from Lowes, and have just this summer rooted three more plants just from leftovers cut for cooking.

I find that the soft "wood" from 4-5" back from the tip root the best. I make sure the leaves from the bottom 2" are removed, and I keep them in a jar of water on the kitchen windowsill until I see plenty of roots. Then I put them in a small pot with regular potting soil and set them on the front porch. I found that for the first few days it is helpful to set the entire pot in a cool-whip container full of water so that they can get used to growing in a different medium. I take them out occasionally to drain, but if they get droopy, I'll set them in the water again for a day or two.

After new growth starts, I move them into a slightly sunnier part of the flower bed, but since the pots are still so small, I have to water them every day. Once the roots start coming out of the drainage holes, I repot them in the urn in which I plan to keep the bush in the sunny herb bed, or give them away.

For Lavender and Rosemary I just shove any cutting with a green tip and slightly to fully woody base into the ground and walk away; doing this procedure anytime from spring to fall. I have about a 50% take with no fuss, no watering, and no tending. I also at times take cuttings, strip the bottom leaves, push into moist potting soil in a small paper drinking cup, and "greenhouse" them in a large closed plastic box for a few weeks to a month. There's about a 90% success rate with the greenhouse method...but you do need to watch that your moisture levels don't build overmuch and rot the slips.

I don't know about the olive and bananna shrubs; but I have used the outdoor method of trimming a small 6" or so slip and pushing it into moist ground to root: boxwood, forsythia, rosemary, lavender, tomato, basil, and viburnum.