Most matter in deep space is individual ions, atoms, or molecules, so has no well-defined phase. Then there's solid dust particles which are made of all sorts of stuff including silicates, organic compounds, and ices of different elements.

Solid. Everything except hydrogen and helium would be in a solid state I think.

That’s not obvious because of the ultra low pressure.

Agreed. I haven’t thought about this stuff since taking gen chem in college, so I went and looked up the phase diagram for Neon, as an example.

At low pressures, it looks like as little as 15 Kelvin is enough to make Neon a gas.

However, deep space is 2.7 Kelvin. Though of course it gets much hotter near stars and even simply being inside a galaxy is enough to hit 10-20 Kelvin.