When I use to run on the treadmill I would get the same feeling.  I no longer use a treadmill, because when it comes time to run on the road, its like you never had one bit of training.  I would advise to stay off the treadmill if you are planning on doing a 5k or 10k etc.....

When I used to run on the treadmill, as soon as I got done with my run I would immediately go outside and walk about 3 blocks to get that shaky feeling out of your legs and it seemed to work like a charm.

I don't find running on the treadmill all that much different than outside.  I did all of the C25K on a treadmill except W7D1 and W9D3.  I complete those two outside, and that was entirely thanks to the time I spent on the treadmill.  The exercise is the same, it takes the same amount of effort (wind resistance in most locations isn't much).  It's a lot more boring, but it's just not accurate to say that it doesn't help you train, because it does.

As for the weird sensation, I get that too for a few seconds, it's a little weird.

I've had this sensation after finishing a run on the treadmill.  I'm not sure why it happens, though I'm sure that running for an extended period of time in the same fixed position at generally the same speed has some effect on it.  For me, it's gone away after a few minutes, usually by the time I've finished stretching, and sooner if I've really taken the time to cool down by walking immediately following my run.