On the going-forwad subject: The J-stroke is useful, yes, but it is not the end-all of forward momentum. I use the J-stroke only on flatwater, when I've got somewhere to go, but am in no hurry. In most any other situation I use alternating forward strokes: that is, I'll take a stroke on my on-side, then a stroke on my off-side, then a couple strokes on my-onside, etc. After a bit of practice, you can get the ratio to about 3:1 on-side/off-side. The other thing, that I also do subconsciously all the time, edge the boat. If you edge to your paddle-side, the chine of your boat forms a keel that will counteract the spinning effect of your forward stroke. A good drill to practice this with is paddling in a circle, edging to the inside of that circle, and paddling only on the inside of the circle. You can adjust the diameter by playing with how far you tilt your boat, and how hard you paddle.
Going backwards is similar, but harder. You get your momentum from an on-side backstroke, and then correct the spin with a crossbow draw. The other, slightly harder option is a backwards D-stroke (or C-stroke, depending on who you talk to). The idea is that you will reach underneath you boat to do your backstroke, so the force is applied in the centre, as opposed to at one side, and so you won't spin much, if at all.
If you want to move straight to your offside, an offside sculling draw is your best bet. A pry will work as well, but if you're prying your paddle is vertical, and if anything unexpected happens, you'll find it trapped deep in the water, and useless. Also, if the unexpected thing is a strong current coming from your onside, the paddle blade will catch that current and flip you to your onside.
As for crossing eddylines, there's nothing special involved. Just use lots of speed, and be very aggresive. When kneeling you can lean forward much farther, and can get more power on one stroke. I take my last stroke right on, or sometimes almost past, the eddyline, and initiate the turn with the edge of my boat, not my paddle. My paddle just helps me hold an angle in a ferry, keep more speed, or accelerate the turn, it's by no means crucial to the manouever.
Hope this helps