I was fighting in Nether Fortress and I held Sharpness sword instead of Smite sword. But I killed
Wither Skelly and normall Skelly with Sharpness 5 with only 2 hits instead of 3. I tried it in other worlds and the same thing happened, so Sharpness works even with Skelly Horse and Stray. Sharpness shouldn't work with undead mobs. It doesn't affect Zombies (including their variants),Phantoms and Withers.

That's it. And yes, I don't have the strength effect.