Can I move /home to another hard disk?

Your system will never look into /oldhome again. You can delete it safely. You are being confused by this statement:

Moving the /home won’t move system files that reside in the root partition.
The root partition files that I referred to are not in /home (or in /oldhome). They are elsewhere and the system knows where they are. Since the files I was referring to aren’t in /oldhome, you can delete /oldhome.