Do I have to use storm & sound in oblivion, or does all natural cover that? Judging by natural interior it should cover also these sounds but I dunno

No, AN does not do what Storms and Sound does. You'll need both if you want those features.

I don't know what Storms and Sounds does exactly as I have never used it. I only use AN and I occasionally hear thunder and see lightning flashes inside buildings. I am not sure where that's coming from if it is not AN. I do have a lot of mods installed but Storms and Sounds is definitely not one of them.

Storms and Sound adds different types of lightning strikes, new thunderstorm sounds, etc, and (the reason I run it) interior weather sounds. So, it sounds like rain is falling on roofs and stuff. Neat stuff.

Exactly that. Is storm & sound obsolete if I use natural interiors? That's what I'm looking to find out.

Not at all. NI enhances S&S, it does not replace it.