There are actually a number of different techniques that are used to estimate the distances of various astronomical objects. You can study the spectrum of the light (or any electromagnetic emission) from that object, and determine how much of a Doppler red shift there is (it's almost always a red shift, very few objects are approaching the Earth) and since the general rate of expansion of the universe is known, we can determine from the size of the red shift how far away something is. If the nebula is associated with a Cepheid variable star, then from the rate of variation and the brightness of the star, we have another clue. And, if we observe the nebula at two different seasons of the year, when the Earth is at opposite sides of the solar system, we may be able to get some parallax for a geometrical calculation, but that depends upon how far away the nebula is; if it is extremely far away, we don't have enough parallax to do it.
The distance from Earth is about 6,500 light years (2000 parsecs).
6500 light-years.
The Orion Nebula is a distance of 1,344 ± 20 light years from the Earth. Based on the plus or minus 20 light years, it doesn't matter if you measure from the Earth or the Sun. The accuracy is within the tolerance range.
to what?
Wikipedia lists the distance as 1,344±20 light-years.
The Crab Nebula is within our own Milky Way Galaxy, but at a distance of about 6500 light years from Earth.
Distance to center of Milky Way: about 26,000 light-years. Distance to Orion Nebula: about 1,300 light-years.
The Earth isn't in a nebula of any sort.
Earth is IN a galaxy - as is the nebula.
Parallax is the method that astronomers use to measure the distance from the sun to the earth.
Celsius is a measure of temperature, not distance.
From what I know you measure it with lightyears.