Back then, at least, the scrapping followed a process like this:
1. The ships fittings, ranging from chairs, paneling, light fixtures, and other items are stripped and sold at auction. (Not sure about the teak on the exterior decks)
2. The scrapping begins with the removal of the superstructure, upper decks, funnels, etc. Basically, the ship is demolished from the top down. (Although sometimes they start from the bow or stern)
3. In the Olympic's case, the hull was partially scrapped and then moved to Inverkeithing for final demolition since Jarrow did not have the necessary facilities to complete the scrapping.
The steel removed from the ship is melted down in furnaces before being recast and reused. Much of Olympic’s steel was used for common items, I believe, and not anything particularly special. (I remember reading about what it was used for, but can’t recall anything else.)
The scrapping of a ship is actually a complex process because great care must be taken to make sure the remains of the ship do not capsize as material is removed.
Brent