I have a very cheap engineered hardwood floor that was destroyed by high heel shoes. It needs to be replaced. It is glued down to Advantech OSB. I have been told this will be a nightmare to remove. I was then told just to nail down 3/4" oak over the top of the old floor. The old floor is 3/8" thick. What should I do? Thanks

Ya, most likely you will be replacing the subfloor panels also, if you decide on removal, and the cost associated with it.

I agree, if it were my house, I'd be trying real hard to convince myself to go over it.

I have torn out glued down engineered flooring for $2 per sf. It was the hardest work I have done. I won't do it for less than $4 now. Go over it!

remove the osb and the floor.
Easy and fast... also not too expensive. What you save in labor will more than compensate for the installation of osb.
Raising the floor another 3/8" to 3/4" may cause other problems, such as at doorways, thresholds, neighboring/adjacent flooring.