Well, smoke is particulate pollution, essentially, which isn't really a big deal. I don't think there are any significant performance issues that would arise in smoky air, unless it is really really bad, in which case there could be a drop in power if there wasn't enough oxygen to combust the fuel. All told, though, there shouldn't be issues with that. There might be some dirt buildup of some sort inside the engine or other abrasion, but still... not a big deal I don't believe.
As for volcanic ash, that is a whole different story. Since that is little bits of rock, there are serious damage issues with abrasion, because it is kind of like sanding down the inside of the engine. In addition, the ash can become hot enough in the engine that it will liquefy, and then you essentially have volcanic magma floating around in the engine, which can lead to a buildup of rock in there, which causes the engine to stop running altogether. It's as if someone had poured concrete into the engine, essentially.
Twin Cessna 812 Victor, Minneapolis Center, we observe your operation in the immediate vicinity of extreme precipitation