What state of matter are nebulae in? After doing research it said that nebulas are made of gas and dust. Are they actually gases and solids, or are they plasma?
Nebulas are not static objects - they evolve.

Initially a nebula might contain mostly (as an example) hydrogen, helium and some other elements in a cloud, but over time that material will clump together to form larger and/or denser material.  Eventually parts of some nebula can even condense enough to form a star and it's planets.  Our solar system was (probably) once part of a nebula.

So there's no single answer to your question.  They can contain most forms of matter.