Considering I have enough strength and the pole has a 6" diameter and is 100 miles long, I lifted the pole to be straight up and down. Now, the pole would extend to be both in outer space and on Earth. Considering the space at which the pole is is vaccuum, would the pole tilt back down to Earth if I were to let go, fly off the Earth, or stay perfectly stationary?
[contented edited by ILP]
One hundred miles up is not nearly far enough to ask this question meaningfully. At a hundred miles, the thing will just fall.
Are you under the misapprehension that gravity only applies within the Earth’s atmosphere?
A good introduction to this type of exercise is found in Kim Stanley Robinson’s “Mars” trilogy (Red Mars, Green Mars, and Blue Mars), in which human beings construct a “skyhook” extending from a high plateau near the Martian equator to a space station in synchronous orbit. That is, they placed a space station in an orbit with a period matching that of the Martian day (for Earth, this is a 24-hour orbit), and strung a cable from the station to the Martian surface, with an elevator running up and down. Thus they were able to bring people and trade goods from space to the surface or from the surface to space much more cheaply than doing it with rockets.
Even on Mars, which has rather lower gravity than Earth, a synchronous orbit is quite a distance from the surface. The space station in the story had to change its position constantly to avoid the cable colliding with Mars’s two moons, Deimos and Phobos.
Now the thing works at all because of tidal forces. Assume we did the same thing on Earth. What we would do is put our space station in geosynchronous orbit, but somewhat outward. Remember that the space station has to keep a tension in the cable - if we put the station exactly in synchronous orbit, the weight of the cable will pull it down and the thing will crash and burn spectacularly. So we increase the orbital altitude slightly, and sink the Earthside end of the cable into a massive single piece of bedrock. Now the station is “hanging” off the Earth, “swinging” at the end of its tether.
So, now we restate your question in these terms: what would it take for a pole long enough to reach from the ground to a distance past geosynchronous orbit, to “balance” where it sits? Either one needs a weight on the end, approximately at geosynch altitude, or the pole itself needs to be rather longer, to balance the gravitational and tidal forces. If we balance the thing properly, one can imagine a pole floating permanently a few inches off the ground, and with a good shove, even a scrawny individual can literally fling it into space. 
Covering my ass because I knew someone would say, “but thats not nearly far enough to ask this question meaningfully”
Then you must take into account that the orbit will still be existent somewhere along the the pole, so would it be kind of like a lever and fulcrum being the orbit point?
That analogy works adequately, I think. Another model is to picture a magnetized iron bar suspended between two magnets, so that it is attracted to each one and thus in some form of limbo. The stability of the system increases greatly when we allow the bar to be long enough to touch each of the magnets.
[contented edited by ILP]
If you don’t understand it abgrund, please let others answer without your interference