You said you're playing on a "X". Is that One X or Series X?
On One X, Oblivion and Skyrim are both 30fps titles. Skyrim supports mods and there's a mod that will unlock the framerate. It doesn't reach 60 constantly on One X and I had some tearing, but it was a slightly better experience than vanilla.
On Series X, that Skyrim mod will allow it to hit 60 all the time (don't quote me on that). However, Microsoft's FPS Boost technology is supposed to be applied to a range of Bethesda games (Skyrim was one of those mentioned) in the future, making 60 a lock. No word yet on Oblivion. Probably will remain at 30fps, although it did get an X Enhancement patch, so it runs at native 4k.