Don't worry about such factors. Our use of those things can have serious effects locally and regionally, but the geophysics is not in danger.
"Does oil serve a purpose for the earth? Does it have a unique purpose in keeping the earths parts lubricated and functioning properly?"
Oil is believed to be a natural fossil product of many billions of creatures' bodies which were entombed long ago under sediments. There has been some suspicion that some oil is made through non-organic geologic processes, but the great majority is seen as from buried organisms. None of my training in geology has suggested that the oil actually lubricates anything where it is found. Admittedly it takes up space, and can have a lot of pressure behind it. (That's why the typical portrayal of an oil strike shows oil exploding from the ground) There have been oil engineers concerned about the possibility of lowering the land surface by oil extraction, but I don't know of any definite data on that.
"When we burn the oil is the earth losing mass becoming less symmetrical? With over mining and logging of heavy metals and woods are we changing the perfect balanced weight of the earth? Will the earth one day fall out of orbit and go crashing into outer space do to anti-symmetries?"
Firstly, while mining and lumbering moves what we naturally perceive as a lot of material, the Earth's total mass of about 6,000,000,000,000,000,000,000,000 kilograms is around 4400 times the total mass of the oceans, and the oceans are a lot more than all the matter that humans have moved so far. Volcanic eruptions have repositioned much more.
Man has not been able yet to delve into the Earth's rock deeper than ten miles or so. The center is around 4000 miles down. The pressures and temperatures become so high that the rocks deform like silly putty. That, I believe is why the Earth is basically a ball; a slightly flattened sphere. Gravity causes that pressure, which causes the material (it's guessed to be metal; nickel and iron, at the core) to become round.
Oil is also a very small part of the whole. What it does once we have it above ground is more important than what it did underground. Of course, it isn't always underground. Check out the La Brea tarpits, in the Los Angeles, California, metro area where slimey oil comes to the surface naturally and has been a deathtrap for millions of creatures for thousands of years. When the oil is burned, or the rocks are crushed, they become more able to reach an equilibrium state, being gaseous, or fine solids able to be moved by water. Such action actually would tend to make the planet more symmetrical. I'm not sure that is a desirable end, but I am sure the difference is very minor on a planetary scale.
The moving of stuff around the surface of the Earth cannot do anything we would notice to the mechanics of the Earth's orbit. All the material, whether we refine it, burn it, or combine it with other stuff and build cities with it, is still part of the mass of the Earth. (Admittedly, a few hundred tons have gone into space, but the meteors landing on the planet easily make up for that)
The Earth will not fall out of orbit because of our actions on Earth. Our concern should be for good stewardship avoiding poisoning of the environment. Do that, and geologic and astrophysical forces will take care of themselves.
