From this question in World Building, it is speculated that planets in nebulas are not greatly affected by the presence of the nebula. This being the case, how do we know that the earth itself is not in a nebula? Has this been tested?
This depends a lot on exactly how you define a nebulae, but we are actually in a very dense region of the interstellar medium, the local interstellar cloud.
Observing it directly from Earth is very difficult, due to sunlight and the solar wind, but its magnetic field has been measured by the Voyager 2 probe.
Assuming it is mostly hydrogen and helium, there are only about 1-2 ng/km³, so it is not a lot to observe. The actual properties of the cloud are still very uncertain.