SUCCESS! Thanks Lawrence!! It took me ~2 hours but I really took my time figuring things out (and taking pics). Here's the before pic, with the sway link "dangling":
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The new (MOOG K750257) and old parts compared:
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And finally the top and bottom views of it installed:
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I hope the pictures can help everyone out in need of changing these.
First, jack up the car and remove the wheel. Then drop the exhaust. For me, the hardest part was dropping the exhaust. You'll need to drop the exhaust only if you're working on the rear passenger link. That means unhooking the exhaust from these gigantic rubber bands underneath the car. There's two of them; 1 right below the bumper and another just a little further up. I learned this can be simplified by using a copious amount of detergent to lube, then a flat head screwdriver to expand that rubber band to finally unhook. It was probably harder for me because of the all rust that developed on that metal rod.
After the exhaust is out of the way, the photo lsettle posted with the vise-grips explained it best; just clamp the bolt directly behind the sway bar and loosen the nut with a socket wrench. I needed a breaker bar for this so keep that in mind; a little WD-40 also helps.
When you're done with the nut, the old sway bar link should come right out and then just put your new one in and install the new nut on top; you'll need an 18mm wrench to hold the bolt (just like the vise-grip did) as you tighten that top nut. Insert the bushings as shown by lsettle's pic. There should be one bushing on each side of the metal plate (arm). By the way, it looks like there's no difference in the part if you're replacing the rear left or right sway bar link.
I used another jack to raise the arm a little bit so i can tighten the 2nd nut from the bottom of the car. Tighten that bottom nut until it wont tighten.
Mount the exhaust back on to its two "rubber bands". It's easier than taking it off, just be sure to put some detergent/lube on that rubber band before you force that rod back in. I did the bumper one first, then the inner one last; seemed easier that way.
Pop the wheel back on and you're good to go.
Thanks to Lawrence (lsettle), JTRAV and the wonderful community of RAV4world for everything. :thumbs_up: