replacing smd atmega328p on a arduino nano clone
You have probably got the "divide clock by 8" fuse set (that is the default). I have a bootloader uploader sketch that you can run on another Arduino that should upload the bootloader, and the first thing it does is fix up that fuse bit. You don't need to remove the oscillator. The default is to not use it, but it doesn't hurt to have it in circuit.