"Submerged density" might also refer to what's more often called "submerged unit weight" or "bouyant unit weight," which is the total weight of the material (including solids and pore water) minus the unit weight of water. This is what a cubic foot would weigh if it and the scale were under water.
"Drained" and "undrained stress" are also terms that don't quite fit conventional usage, and out of context, their meanings aren't obvious to me. I'd guess they mean "effective stress" and "total stress." Effective stress is the unifying concept of soil mechanics. It governs shear strength, compressibility, elastic properties, etc. You should probably find an undergrad soil-mechanics text.
Bon chance!
DRG