What is the oldest sediment?
According to page 86 of Exploring the World Ocean:


  In December 1989, ODP scientists drilled Hole 801C
  and recovered Jurassic-age rocks and sediments, about
  170–165 million years old, from the Pigafetta Basin in
  the western Pacific, near the Mariana Islands. Sediments
  of nearly identical age had been found previously from
  the Deep Sea Drilling Project Hole 534A, located on the
  Blake-Bahama basin in the central Atlantic. These sediments
  and the rocks on which they rest are among the
  oldest oceanic crust found in the world ocean.


There is a more-detailed discussion at Site 801: Sedimentology and Biostratigraphy